How to verify this limit? Kindly asking for any hints about showing:
$$\lim_{n\to\infty}\int_0^1\frac{dx}{(1+x/n)^n}=1-\exp(-1)$$
Thank you very much, indeed!

Another way:
The sequence of unctions $\frac {1}{(1+x/n)^n}$ is dominated by the integrable function $g$ (where $g(x)=1$ for all $x\in [0,1]$, now you can use Lesbesuge dominated convergence theorem.
