I was given a problem at the university.
Compute the limit
$\displaystyle\lim_{n\to \infty}\left(\sum_{k=1}^n \frac{1}{{n}\choose {k}}\right)^n$ .
$\displaystyle\sum_{k=1}^n \frac{1}{{n}\choose {k}}=\frac{1}{n}+O(\frac{1}{n^2 })...+1$. I wonder if it's possible to use $(1+\frac{1}{n})$ instead of the sum. Then we get e=2.718... Am I right?
