# How do you find the sum of the infinite geometric series given 3/2-3/4+3/8-...?

Sep 14, 2017

${S}_{\infty} = 1$

#### Explanation:

$\text{the sum to n terms of a geometric sequence is}$

•color(white)(x)S_n=(a(1-r^n))/(1-r)

$\text{where a is the first term and r the common ratio}$

$\text{as "ntooo,r^nto0" and sum becomes}$

S_oo=a/(1-r)color(white)(x);|r|<1

$\text{here "a=3/2" and } d = - \frac{3}{4} \times \frac{3}{2} = - \frac{1}{2}$

$\Rightarrow {S}_{\infty} = \frac{\frac{3}{2}}{1 - \left(- \frac{1}{2}\right)} = 1$