# Tagged Questions

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### How to find that a number is a sum of multiple of different numbers?

Suppose a product comes in packs of 3, and 5, and a customer demands 8 quantities of that ...
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### A closed form for $1^{2}-2^{2}+3^{2}-4^{2}+ \cdots + (-1)^{n-1}n^{2}$

Please look at this expression: $$1^{2}-2^{2}+3^{2}-4^{2} + \cdots + (-1)^{n-1} n^{2}$$ I found this expression in a math book. It asks us to find a general formula for calculate it with $n$. ...
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### Aproximation for the variance (sum)

Given that we know The mean of a population $\tilde W(t) = \sum_{i=1}^{n}f_{i}(t)*W_{i}$ The variance of the population in the previous step $Var(0) = \sum_{i=1}^{n}f_{i}(0)*(W_{i}-\tilde W(0) )$ ...
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### Find the integer part of the sum $S=\sum_{k=1}^{80} \frac{1}{\sqrt k}$

Let $$S=\sum_{k=1}^{80} \frac{1}{\sqrt k}.$$Then I would like to obtain $\lfloor S \rfloor$, the integer part of $S$. I am not able to think how to start question .
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### Compute $\sum\limits_{k=0}^{100}\frac{1}{(100-k)!(100+k)!}$

$$\sum_{k=0}^{100}\frac{1}{(100-k)!(100+k)!}$$ My work $$\sum_{k=0}^{100}\frac{2n!}{(2n!)(n-k)!(n+k)!}$$ $$\sum_{k=0}^{100}\frac{^{2n}C_{n-k}}{(2n!)}$$ $$\sum_{k=0}^{100}\frac{^{2n}C_{n+k}}{(2n!)}$$...