For the series $\sum_{r=1}^{\infty}\frac25\left(-\frac13\right)^{r-1}$, decide whether it converge

Question

For the series $\sum_{r=1}^{\infty}\frac25\left(-\frac13\right)^{r-1}$, decide whether it converges. If it does, find its sum.

Accepted Answer

converges to $\frac3{10}$

Convergence and sum to infinity