# Tagged Questions

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### Double summation of elementary functions

I am finding some trouble on calculating the following double summation: $\sum_{k=1}^\infty \frac{b^k}{k!k}\sum_{n=0}^{k-1}\frac{(b*x)^n}{(n-1)!}$ Note that the inside sum gives: ...
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### Double summation including power and factorial [duplicate]

I am finding some trouble in computing the following sum: $$\sum_{k=0}^\infty \frac{x^k}{k!}\;\sum_{m=0}^k\frac {y^m}{m!}$$ Could you please provide a result? Thanks in advance
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### factorial Vs power sequence

What sequence is dominant between $f(n) = n!$ and $g(n) = 2^n$ or (or $a^n$) I mean $f/g -> 0$ or $infinity$
### How to find the last non-zero digit in ${^n\!P_k}$?
What is the procedure of finding the last non-zero element in ${^n\!P_k}$?
### Is it true that $n> a^2\Rightarrow n!>a^n$, $n\in\mathbb{N}, a\in\mathbb{R}$?
If so, how can it be proven? (I have evaluated it up to $n=25$.) If not, does there exist a $k\in\mathbb{R}$ such as that $n> a^k\Rightarrow n!>a^n$, with $n\in\mathbb{N},a\in\mathbb{R}$? It ...