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КАТАР (математикалык туюнтма) - Түзөтүүлөр тарыхы
2026-04-23T15:42:20Z
Уикидеги бул барактын өзгөртүү тарыхы
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Temirkan: Temirkan moved page КАТАР 1 to КАТАР (математикалык туюнтма)
2025-12-10T03:33:33Z
<p>Temirkan moved page <a href="/index.php?title=%D0%9A%D0%90%D0%A2%D0%90%D0%A0_1&action=edit&redlink=1" class="new" title="КАТАР 1 (мындай барак жок)">КАТАР 1</a> to <a href="/index.php/%D0%9A%D0%90%D0%A2%D0%90%D0%A0_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%D0%BB%D1%8B%D0%BA_%D1%82%D1%83%D1%8E%D0%BD%D1%82%D0%BC%D0%B0)" title="КАТАР (математикалык туюнтма)">КАТАР (математикалык туюнтма)</a></p>
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<td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">03:33, 10 Декабрь (Бештин айы) 2025 -деги абалы</td>
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Temirkan
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Temirkan, 03:33, 10 Декабрь (Бештин айы) 2025 карата
2025-12-10T03:33:01Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Мурунку нускасы</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">03:33, 10 Декабрь (Бештин айы) 2025 -деги абалы</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">1 сап:</td>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><b type='title'>КАТАР</b> – белгилүү бир маанини берген <del style="font-weight: bold; text-decoration: none;">матем.</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><b type='title'>КАТАР</b> – белгилүү бир маанини берген <ins style="font-weight: bold; text-decoration: none;">математикалык </ins>символдордон турган <i>а</i><sub>1</sub>, <i>а</i><sub>2</sub><i>, ..., а<sub>n</sub>, ...</i> удаалашты&shy;гынын <ins style="font-weight: bold; text-decoration: none;">алгебралык </ins>суммасы <i>а</i><sub>1</sub>+<i>а</i><sub>2</sub><i>+...+ а<sub>n</sub>+...</i> (*) түрүндөгү туюнтма. <ins style="font-weight: bold; text-decoration: none;">Катардын </ins>мүчөлөрү сан, же функция, же вектор, же матрица ж. б-ды белгилеши мүмкүн. Ушуга жараша <ins style="font-weight: bold; text-decoration: none;">катар </ins>сандуу, функциялуу, <ins style="font-weight: bold; text-decoration: none;">векторлуу</ins>, матрицалуу ж. б. деп аталат. <ins style="font-weight: bold; text-decoration: none;">Катардын </ins>(*) түрүндөгү кеңейтилип жазылышынын ордуна L<i>an</i> түрүндөгү кыскартылган белгилөө <ins style="font-weight: bold; text-decoration: none;">колдонулат. Эгер lim L </ins><i><ins style="font-weight: bold; text-decoration: none;">Sn = S</ins></i> <ins style="font-weight: bold; text-decoration: none;">деген акыркы чекке ээ анда ал жыйналуучу катар деп, ал эми</ins></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>символдордон турган <i>а</i><sub>1</sub>, <i>а</i><sub>2</sub><i>, ..., а<sub>n</sub>, ...</i> удаалашты&shy;гынын <del style="font-weight: bold; text-decoration: none;">алг. </del>суммасы <i>а</i><sub>1</sub>+<i>а</i><sub>2</sub><i>+...+ а<sub>n</sub>+...</i> (*) түрүндөгү туюнтма. <del style="font-weight: bold; text-decoration: none;">К-дын </del>мүчөлөрү сан, же функция, же</div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>вектор, же матрица ж. б-ды белгилеши мүмкүн. Ушуга жараша <del style="font-weight: bold; text-decoration: none;">К. </del>сандуу, функциялуу, <del style="font-weight: bold; text-decoration: none;">вектор-</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">луу</del>, матрицалуу ж. б. деп аталат. <del style="font-weight: bold; text-decoration: none;">К-дын </del>(*) түрүндөгү кеңейтилип жазылышынын ордуна</div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">оо</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>L<i>an</i> түрүндөгү кыскартылган белгилөө <del style="font-weight: bold; text-decoration: none;">колдо-</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><i><del style="font-weight: bold; text-decoration: none;">n</del></i><del style="font-weight: bold; text-decoration: none;">=1</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">нулат. Эгер</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><i>S =а +а +...+ а <ins style="font-weight: bold; text-decoration: none;">катардын</ins></i> толук эмес суммасы деп аталат. Эгер <ins style="font-weight: bold; text-decoration: none;">катардын </ins>толук эмес суммасы <i>S<sub>n</sub></i></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">lim L <i>Sn = S</i> деген акыркы чекке ээ</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"><i>n</i>--.оо</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><i>S =а +а +...+ а</i></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">К-дын </del>толук эмес суммасы деп</div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"><i>n</i> 1 2 <i>n</i></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>аталат. Эгер <del style="font-weight: bold; text-decoration: none;">К-дын </del>толук эмес суммасы <i>S<sub>n</<del style="font-weight: bold; text-decoration: none;">sub><</del>sub></i<del style="font-weight: bold; text-decoration: none;">></sub</del>></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>удаа-</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>удаа-</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>лаштыгынын акыркы чеги жок болсо, анда ал жыйналбас <del style="font-weight: bold; text-decoration: none;">К. </del>деп аталат. <del style="font-weight: bold; text-decoration: none;">Мис.</del>, чексиз кемүүчү</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>лаштыгынын акыркы чеги жок болсо, анда ал жыйналбас <ins style="font-weight: bold; text-decoration: none;">катар </ins>деп аталат. <ins style="font-weight: bold; text-decoration: none;">Мисалы</ins>, чексиз кемүүчү <i>a +a q+a q</i><sup>2</sup>+...+<i>a q<sup>n</sup>...</i> <ins style="font-weight: bold; text-decoration: none;">геометриялык </ins>прогрессия <ins style="font-weight: bold; text-decoration: none;">жыйналуучу катар</ins>, мында |<i>q</i>|<1, анткени <i>S</i> = lim <i>Sn =</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><i>a +a q+a q</i><sup>2</sup>+...+<i>a q<sup>n</sup>...</i> <del style="font-weight: bold; text-decoration: none;">геом. </del>прогрессия <del style="font-weight: bold; text-decoration: none;">жыйна-</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">1 1 1 1</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"><i>a</i></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">луучу К.</del>, мында |<i>q</i>|<1, анткени <i>S</i> = lim <i>Sn =</div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>n</i>--.оо</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>n</i>--.оо</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>1</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>1</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>1 - <i>q</i></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>1 - <i>q</i></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>(чексиз кемүүчү <del style="font-weight: bold; text-decoration: none;">геом. </del>прогрессиянын суммасы),</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>(чексиз кемүүчү <ins style="font-weight: bold; text-decoration: none;">геометриялык </ins>прогрессиянын суммасы), ал эми 1–1+1–1+...+1</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"><i>n</i>–1</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>ал эми 1–1+1–1+...+1</div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>+... сан удаалаштыгы</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>+... сан удаалаштыгы</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>жыйналбас <del style="font-weight: bold; text-decoration: none;">К.</del>, анткени толук эмес сумманын</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>жыйналбас <ins style="font-weight: bold; text-decoration: none;">катар</ins>, анткени толук эмес сумманын <i>S</i><sub>1</sub>=1; <i>S</i><sub>2</sub>=0; <i>S</i><sub>3</sub>=1; <i>S</i><sub>4</sub>=0, ... удаалаштыгынын чеги жок.</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><i>S</i><sub>1</sub>=1; <i>S</i><sub>2</sub>=0; <i>S</i><sub>3</sub>=1; <i>S</i><sub>4</sub>=0, ... удаалаштыгынын чеги жок.</div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Ад.: <i>Маркушевич А. И.</i> Ряды. Элементарный очерк. М., 1957; <i>Фихтенгольц Г. М.</i> Основы математического анализа. Т. 2. М., 1964.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Ад.: <i>Маркушевич А. И.</i> Ряды. Элементарный очерк. М., 1957; <i>Фихтенгольц Г. М.</i> Основы математического анализа. Т. 2. М., 1964.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Категория:4-том, 154-203 бб]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Категория:4-том, 154-203 бб]]</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
</table>
Temirkan
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Kadyrm: 1 версия
2025-10-06T16:00:19Z
<p>1 версия</p>
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<td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">16:00, 6 Октябрь (Тогуздун айы) 2025 -деги абалы</td>
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Kadyrm
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vol4>KadyrM, 09:54, 6 Октябрь (Тогуздун айы) 2025 карата
2025-10-06T09:54:02Z
<p></p>
<p><b>Жаңы барак</b></p><div><b type='title'>КАТАР</b> – белгилүү бир маанини берген матем.<br />
символдордон турган <i>а</i><sub>1</sub>, <i>а</i><sub>2</sub><i>, ..., а<sub>n</sub>, ...</i> удаалашты&shy;гынын алг. суммасы <i>а</i><sub>1</sub>+<i>а</i><sub>2</sub><i>+...+ а<sub>n</sub>+...</i> (*) түрүндөгү туюнтма. К-дын мүчөлөрү сан, же функция, же<br />
вектор, же матрица ж. б-ды белгилеши мүмкүн. Ушуга жараша К. сандуу, функциялуу, вектор-<br />
луу, матрицалуу ж. б. деп аталат. К-дын (*) түрүндөгү кеңейтилип жазылышынын ордуна<br />
оо<br />
L<i>an</i> түрүндөгү кыскартылган белгилөө колдо-<br />
<i>n</i>=1<br />
<br />
нулат. Эгер<br />
lim L <i>Sn = S</i> деген акыркы чекке ээ<br />
<i>n</i>--.оо<br />
<br />
<i>S =а +а +...+ а</i><br />
К-дын толук эмес суммасы деп<br />
<br />
<i>n</i> 1 2 <i>n</i><br />
аталат. Эгер К-дын толук эмес суммасы <i>S<sub>n</sub><sub></i></sub><br />
удаа-<br />
<br />
лаштыгынын акыркы чеги жок болсо, анда ал жыйналбас К. деп аталат. Мис., чексиз кемүүчү<br />
<i>a +a q+a q</i><sup>2</sup>+...+<i>a q<sup>n</sup>...</i> геом. прогрессия жыйна-<br />
<br />
1 1 1 1<br />
<i>a</i><br />
<br />
луучу К., мында |<i>q</i>|<1, анткени <i>S</i> = lim <i>Sn =<br />
n</i>--.оо<br />
1<br />
1 - <i>q</i><br />
<br />
(чексиз кемүүчү геом. прогрессиянын суммасы),<br />
<i>n</i>–1<br />
<br />
ал эми 1–1+1–1+...+1<br />
+... сан удаалаштыгы<br />
<br />
жыйналбас К., анткени толук эмес сумманын<br />
<i>S</i><sub>1</sub>=1; <i>S</i><sub>2</sub>=0; <i>S</i><sub>3</sub>=1; <i>S</i><sub>4</sub>=0, ... удаалаштыгынын чеги жок.<br />
<br />
<br />
Ад.: <i>Маркушевич А. И.</i> Ряды. Элементарный очерк. М., 1957; <i>Фихтенгольц Г. М.</i> Основы математического анализа. Т. 2. М., 1964.<br />
[[Категория:4-том, 154-203 бб]]<br />
</div>
vol4>KadyrM