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

##### 1 Answer

Sep 14, 2017

#### Explanation:

#"the sum to n terms of a geometric sequence is"#

#•color(white)(x)S_n=(a(1-r^n))/(1-r)#

#"where a is the first term and r the common ratio"#

#"as "ntooo,r^nto0" and sum becomes"#

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

#"here "a=3/2" and "d=-3/4xx3/2=-1/2#

#rArrS_oo=(3/2)/(1-(-1/2))=1#