Convergence of a series with terms

Question

I am trying to find for what value is this this series convergent for:

$$1/3 -1/6 + 1/18 - 1/72 .....$$

Does it have a relation with exponential function?

Answer 1

$$1/3 -1/6 + 1/18 - 1/72 .....=\frac{1}{3}(1-\frac{1}{2!}+\frac{1}{3!}-\frac{1}{4!}+....)=\frac{1-e^{-1}}{3}$$