Q:

How to calculate this limit？

Here is my question:
$\displaystyle\lim_{n\rightarrow \infty}n^2[(1+\frac{1}{1+n})^{n+1}-(1+\frac{1}{n})^{n}]=?$
Any hints will be fine. Thank you!

A:

As simple as using Limit:
Clear[n];
Limit[n^2 ((1 + 1/(1 + n))^(n + 1) - (1 + 1/n)^n), n -> ∞]
(*E/2*)

