Proof divergence $\sum_{n=1}^\infty (\frac{n+1}{n})^n$

Question

Proof divergence $\sum_{n=1}^\infty (\frac{n+1}{n})^n$

I don't know how to do this problem, maybe a hint or two will help.

Answer 1

All what you need to know: $$\lim_{n\to\infty}\left(\dfrac{n+1}{n}\right)^n=\lim_{n\to\infty}\left(1+\dfrac{1}{n}\right)^n=e.$$

Answer 2

The fact that every term is $>1$ is enough to show that it diverges, since the terms do not approach $0$.

(The fact mentioned by حكيم الفيلسوف الضائع in another posted answer here is well worth knowing, but it's overkill for the present question.)