Question

Does the series 3+9+27+81+…. diverge or converge

Answer 1

this series diverges

Answer 2

Given the series

`3+9+27+81+\cdots`

which is a geometric series with first term 3 and common ratio 3.

A geometric series conveges if and only if |r| < 1, where r is the common ratio. Here, r = 3 > 1. So, the given geometric series diverges.