Now, what familiar equations can I use?

Calculus Level 3

\[\large\displaystyle\sum_{n=1}^{\infty}\frac{\left(1-\frac{1}{e}\right)^n}{n}=\ ?\]

With \(\displaystyle e = \sum_{m=0}^\infty \frac1{m!} \approx 2.71828 \).