Question

How do you find the sum of the infinite geometric series `4/25+2/5+1+...` ?

Answer 1

The sum of this series does not converge.

Explanation:

A general term of this series is:

`a_n = (5/2)^(n-3)" "` `n = 1,2,3,...`

Since the common ratio `5/2` is larger than `1` the sum of this series does not converge. In fact it monotonically diverges to `+oo`.