How do you find the sum of the infinite geometric series 5/4-1/4+1/20-1/100+...?

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Answer 1 · 2016-02-07T21:38:58

First, find the common ratio, r.

$r = \frac{t_{2}}{t_{1}}$ $r = t_2/t_1$

$r = \frac{- \frac{1}{4}}{\frac{5}{4}}$ $r = (-1/4)/(5/4)$

$r = - \frac{1}{5}$ $r = -1/5$

Now, we know all we need to know to find the sun, which can be found using the formula $S_{\infty} = \frac{a}{1 - r}$ $S_oo = a/(1 - r)$

$S_{\infty} = \frac{\frac{5}{4}}{1 - (- \frac{1}{5})}$ $S_oo = (5/4)/(1 - (-1/5))$

$S_{\infty} = \frac{\frac{5}{4}}{\frac{6}{5}}$ $S_oo = (5/4) / (6/5)$

$S_{\infty} = \frac{25}{24}$ $S_oo = 25/24$

The sum of the series is $\frac{25}{24}$ $25/24$