Question

How do you find the sum of the infinite geometric series 80+40+20+...?

Answer 1

`160`

Explanation:

Since the common ratio `r=(x_n+1)/x_n=1/2<1`, it implies that this series converges.

Its sum may be given by `s_oo=sum_(r=1)^ooar^(n-1)=a/(1-r)`

`=80/(1-1/2)=160`