Question

How do you find the sum of the infinite geometric series 5+5/6+5/6^2+5/6^3+...?

Answer 1

`sum_(n=1)^oo 5(1/6)^(n-1)=5/(1-1/6)=6`

Explanation:

The common ratio of this geometric series is `r=(5/6)/5=1/6`.

Since `|r|=1/6<1`, it implies that the series converges to `a/(1-r)` where `a=5` is the first term.

This infinite geometric series, as well as its sum, may hence be written in the form

`sum_(n=1)^oo 5(1/6)^(n-1)=5/(1-1/6)=6`.