# All Questions

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### Summation of divergent series of Euler: $0!-1!+2!-3!+\cdots$

Consider the series $$\sum\limits_{k=0}^\infty (-1)^kk!x^k\in\mathbb{R}[[x]]$$ Let $s_n(x)$ be partial sum. And let $\omega_{k,n}=(k!^2(n-k)!)^{-1}$. My question is: Prove that ...
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### Product of two elements is identity implies they are mutual inverses..

Let $A$ be an associative unital n-dimensional algebra over field $F$. Show that if $ab=1$ for some $a,b \in A$ then $a=b^{-1}$
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### Generating random string

I'm working on a small web service that will require users to upload files. The file type is P12. When the file is uploaded and I need to save it on my server, I need to generate a random name for it. ...
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### Computing sign table for $2^k$ factorial experiment design

all! I need to compute the sign table for a generic $2^k$ factorial design. For $k$ factors we compute $2^k$ experiments and need to compute a $2^k \times 2^k$ matrix, as the following example for ...
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