Question

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

Answer 1

See explanation.

Explanation:

This sequence is not convergent, therfore has no finite sum.

A geometric sequence `{a_n}` converges if and only if its quotient `q` is greater than `-1` and smaller than `1`.

The given sequence has `a_1=5/3` and `q=5` The quotient is greater than `1`, so the sequence has no finite sum.