Сумма бесконечно убывающей геометрической прогрессии равна 32, а сумма её первых...

July 2022 1 7 Report

Сумма бесконечно убывающей геометрической прогрессии равна 32, а сумма её первых пяти членов 31. Найдите первый член прогрессии.

Answers & Comments

LilitKit $32= \frac{b1}{1-q}$
$31= \frac{b1(1-q^{5} )}{1-q}$
b1=32(1-q)
$31= \frac{32(1-q)(1-q^{5} )}{1-q}= 32(1-q^{5})$
$q^{5}=1- \frac{31}{32}= \frac{1}{32}$
q=1/2
b1=32(1-1/2)=32 * 1/2 = 16

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