17k views

### Surprising identities / equations [closed]

What are some surprising equations / identities that you have seen, which you would not have expected? This could be complex numbers, trigonometric identities, combinatorial results, algebraic ...
58 views

### Find lim$_{n \to \infty} \sum _{ k =0}^ n \frac{e^{-n}n^k}{k!}$ [duplicate]

We need to find out the limit of, lim$_{n \to \infty} \sum _{ k =0}^ n \frac{e^{-n}n^k}{k!}$ One can see that $\frac{e^{-n}n^k}{k!}$ is the cdf of Poisson distribution with parameter $n$. Please ...
### Closed Form for $~\lim\limits_{n\to\infty}~\sqrt n\cdot(-e)^{-n}\cdot\sum\limits_{k=0}^n\frac{(-n)^k}{k!}$
$\qquad\qquad\qquad$ Does $~\displaystyle\lim_{n\to\infty}\frac{\sqrt n}{(-e)^n}\cdot\sum_{k=0}^n\frac{(-n)^k}{k!}~$ possess a closed form expression ? Inspired by this frequently asked question, ...