Is this series convergent or divergent? $\frac{n}{1+e^{-n}}$ I don't know what to do. I was thinking of root test but I get stuck whenever I do it. Any help will be appreciated
Hint: apply the divergence/trivial test.
Just apply the limit test$$\lim_{n \to \infty} \frac{n}{1 + e^{-n}} = \lim_{n \to \infty} \frac{n}{1 + \frac{1}{e^n}}= \frac{\infty}{1 + \frac{1}{e^\infty}} = \frac{\infty}{1 + 0} = \infty$$

and so since the limit is not equal zero then the series is said to diverge

check this link also 


  http://mathworld.wolfram.com/LimitTest.html