# Thread: Help with a series

1. ## Help with a series

I have the series (from 1 to infinity) of (1-(1/e^n))^n. I can't seem to find a test to help me establish convergence or divergence.

Thanks for your help!

Bret

2. What is the limit at infinity for (1-(1/e^n))^n?
If it is not zero, then it diverges.

3. $$\mathop {\lim }\limits_{n \to \infty } {(1 - \frac{1}{{{e^n}}})^n} = \mathop {\lim }\limits_{n \to \infty } {e^{\ln (1 - \frac{1}{{{e^n}}}) \cdot n}} = {e^{\mathop {\lim }\limits_{n \to \infty } \frac{{ - {n^2}}}{{{e^n} - 1}}}} = {e^{\mathop {\lim }\limits_{n \to \infty } \frac{{ - 2}}{{{e^n}}}}} = 1$$

4. Thanks everyone. I get really embarassed when I forget basic things. Cool explanation Pranas. Thanks also snowtea.