# How do you find the sum of the infinite geometric series given 5/3+25/3+125/3+...?

A geometric sequence $\left\{{a}_{n}\right\}$ converges if and only if its quotient $q$ is greater than $- 1$ and smaller than $1$.
The given sequence has ${a}_{1} = \frac{5}{3}$ and $q = 5$ The quotient is greater than $1$, so the sequence has no finite sum.