Найдите сумму бесконечной геометрической прогрессии -4√2; 4; -2√2. Created by vertu345. algebra-ru

Найдите сумму бесконечной геометрической прогрессии -4√2; 4; -2√2...

vertu345 @vertu345

August 2022 1 27 Report

Найдите сумму бесконечной геометрической прогрессии -4√2; 4; -2√2

Answers & Comments

NNNLLL54

Verified answer

$\{b_{n}\}:\; \; -4\sqrt2\; ,\; 4\; ,\; -2\sqrt2\; ,\; ...\\\\q=\frac{b_{n}}{b_{n-1}}\; \; ,\qquad \frac{b_2}{b_1}=\frac{4}{-4\sqrt2}=-\frac{1}{\sqrt2} \; \; ,\; \; \; \frac{b_3}{b_2}=\frac{-2\sqrt2}{4}=-\frac{\sqrt2}{2}=-\frac{1}{\sqrt2}\\\\\frac{b_2}{b_1}=\frac{b_3}{b_2}\; \; \Rightarrow \; \; \; q=-\frac{1}{\sqrt2}\\\\S=\frac{b_1}{1-q}=\frac{-4\sqrt2}{1+\frac{1}{\sqrt2}}=\frac{-4\sqrt2\, \cdot \, \sqrt2}{\sqrt2+1}=-\frac{8}{\sqrt2+1}=-\frac{8\, (\sqrt2-1)}{(\sqrt2+1)(\sqrt2-1)}=-8\, (\sqrt2-1)$

0 votes Thanks 0

Answers & Comments

Verified answer

46f9f3ce7b270e3c935bf6df5d2d8e3f

1cb44ac0e3ede0abb5155d9178c60dc8

c493931798e2dc1999acddba56e073d0

abcfdf1448c7e853a7126ee06a1fe747

600be2918311b0ae4b3eea6032967a57

9f2a5589d20d1eec186fcf54c999e12d

1 3 648da0f8bba4d

f2c56b8036041987ae2d0480fb662853

7c833c9b8ec461ce07b0f2c775eea86f

152fb21ffcf973597947654a019c40a6

рекомендуемые вопросы

Helpful Links

Helpful Social