Чему равно произведение : (1-1/4)(1-1/9)(1-1/16)...(1-1/225)?. Created by ArlanSul. matematika-ru

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ArlanSul @ArlanSul

August 2022 1 8 Report

Чему равно произведение : (1-1/4)(1-1/9)(1-1/16)...(1-1/225)?

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IrkaShevko

Verified answer

$(1- \frac{1}{2^2})(1- \frac{1}{3^2})(1- \frac{1}{4^2})...(1- \frac{1}{15^2})=\\\\
= \frac{(2-1)(2+1)}{2^2} \frac{(3-1)(3+1)}{3^2} \frac{(4-1)(4+1)}{4^2} ...\frac{(15-1)(15+1)}{15^2} =\\\\
= \frac{1*2*3^2*4^2*5^2*...*14^2*15*16}{2^2*3^2*4^2*5^2*...*15^2} =\\\\=
 \frac{1*2*15*16}{2^2*15^2} = \frac{16}{30} = \frac{8}{15}$

Ответ: 8/15

12 votes Thanks 15

dvoe rabochih rabotaya vmeste mogut vypolnit rabotu za 12 dnej za skolko dnej ra

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ArlanSul July 2022 | 0 Ответы

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dvoe rabochih rabotaya vmeste mogut vypolnit rabotu za 12 dnej za skolko dnej ra

poezd prohodit mimo svetofora za 7 sekund a mimo platformy dlinnoj 400 metrov

sistemy sposob slozheniya pod v

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