# Linked Questions

1answer
1k views

### Limit using Poisson distribution [duplicate]

Show using the Poisson distribution that $$\lim_{n \to +\infty} e^{-n} \sum_{k=1}^{n}\frac{n^k}{k!} = \frac {1}{2}$$
2answers
485 views

2answers
27 views

### Central value of the partial exponential function [duplicate]

I need help calculating the central value of the partial exponential function : $$\lim_{n \to \infty} e^{-n} \sum^n_{k=0} \frac{n^k}{k!}$$ fd
1answer
45 views

### Does n power of e grow much more faster than its Maclaurin polynomial? [duplicate]

I wonder how to calculate the following limit: $$\lim_{n\rightarrow\infty}\frac{1+n+\frac{{}n^{2}}{2!}+\cdots +\frac{n^{n}}{n!}}{e^{n}}$$ In the first sight, I think it should be zero, because ...
0answers
33 views

### Compare $e^n$ and its first $n$ terms sum [duplicate]

Compute the limit as $n$ approaches infinity. $$\frac{\sum_{0\le i\le n} \frac{n^i}{i!}}{e^n}$$ It is somehow between 0 and 1.
0answers
29 views

### Limit of Series with Variable Lower Bound [duplicate]

I'm trying to compute the following limit of a series: $$\lim_{n\to\infty} \sum_{k = n+1}^{\infty}\frac{e^{-n}n^{k}}{k!}$$ Factoring $e^{-n}$ out of the sum, applying the definition of $e^{x}$ as a ...
85answers
14k views

### Surprising identities / equations

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 ...

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