Is it possible to show using only elementary facts that:
$ \sum_{k=0}^n \frac{1}{k!} \le \left(1 + \frac{1}{2n}\right)^{2n+1} $
Of course they both have the same limit, $e$, but let's assume I don't know that about series.
I guess that I have to use the fact that $\left(1 + \frac{1}{2n}\right)^{2n+1} = \sum_{k=0}^{2n+1} \binom{2n+1}{k} \cdot \frac{1}{(2n)^k}$?