ГЕОМЕТРИЯЛЫК ПРОГРЕССИЯ

ГЕОМЕТРИЯЛЫК ПРОГРЕ́ССИЯ – сан удаалаштыгы. Ал экинчи мүчөсүнөн баштап, ар бир кийинки мүчөсү өзүнөн мурдагы мүчөнү ушул прогрессия үчүн турактуу Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q\neq0} (прогрессиянын бөлүмү) санына көбөйтүүдөн алынат. Мисалы, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a_1q,a_2q^2, a_3q^3, ... a_nq^n ,..} Эгерде Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q>1} болсо, анда геометриялык прогрессия өсүүчү, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0 < q < 1} болсо, кемүүчү, ал эми Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q < 0} болгондо, геометриялык прогрессиянын белгиси кезектешүүчү деп аталат. Геометриялык прогрессиянын ар бир мүчөсү (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a_i} ), биринчи мүчөсү (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a_1} ) жана бөлүмү (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q} ) аркылуу төмөнкүчө туюнтулат: Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a_i = a_1q^{i-1}} . Мында, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q\neq1} болгондо биринчи Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n} мүчөсүнүн суммасы:Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle S_n={a_1-a_1q^n \over 1-q}={a_1q^n-a_1 \over q-1}} . Эгерде Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left\vert q \right\vert<1} болсо жана Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n} саны чексиз өсүшү менен Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle S_n} суммасы Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle S={a_1\over 1-q}} пределине умтулат. S чексиз кемүүчү геометриялык прогрессиянын суммасы деп аталат. Геометриялык прогрессиянын ар бир мүчөсү мурунку ж-а кийинки мүчөлөрүнүн геометриялык орто санына барабар: Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a_n=\sqrt{a_{n-1}a_{n+1}}} .