# How do you find the sum of the infinite geometric series 8+6+9/2+27/8+...?

Oct 26, 2017

${S}_{\infty} = 32$

#### Explanation:

The sum of infinite GP is given by

${S}_{\infty} = \frac{a}{1 - r}$

where

$a =$the first term

$r =$the common ratio

AND$\text{ } | r | < 1$" "if $\text{ "S_oo" }$is to exist

we need to fin teh common ratio . We do this by

$r = \frac{{u}_{n + 1}}{u} _ n$

$r = \frac{6}{8} = \frac{3}{4}$

$| r | < 1 \text{ ":.S_oo" exists}$

${S}_{\infty} = \frac{8}{1 - \frac{3}{4}}$

${S}_{\infty} = \frac{8}{\frac{1}{4}} = 8 \times \frac{4}{1}$

${S}_{\infty} = 32$