# Tagged Questions

Questions about evaluating summations, especially finite summations. For infinite series, please consider the (sequences-and-series) tag instead.

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### Alternating series of compositions of triangular numbers

I'm modeling a process which involves a subset $S$ of a large number $n_A$ of objects - call them balls. Each time I add a ball to $S$, it may dislodge another ball with probability proportional to ...
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### If $\ (1+3x+x^2)^{10}=\sum_{r=0}^{20}a_r x^r\$ then…

If $$\ (1+3x+x^2)^{10}=\sum_{r=0}^{20}a_r x^r\$$ Then then what is the least number except 1 which divides the following:$$\ \sum_{r=0}^{20}(3r+1)a_r\$$ EDIT: i have put x=1 then it is something ...
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### $\sum_{k=0}^{2016}(1+ \omega^k)^{2017}\$

Let $\omega \$be a root of the polynomial $\ x^{2016} +x^{2015}+x^{2014}+...+x+1=0 \$. Then find the value of the following sum: $$\sum_{k=0}^{2016}(1+ \omega^k)^{2017}\$$ Well I have simplified ...
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### Summation of an expression $\sum_{h=0}^{\ln n}\frac{h}{2^h}$

How can be we get the closed form for this expression? $$\sum_{h=0}^{\ln n}\frac{h}{2^h}$$
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### How to calculate a sum using a geometric series

How to calculate this with a simple calculator. sum_{i=20}^n=59 0.1*600*1.04^(60-i) = ? I tried this but it's wrong. Can somebody please tell me where I made a ...
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### $\sum_{1 \leq i,j \leq n, i|n, j|n} gcd(i,j)$

$$S = \sum_{1 \leq i,j \leq n, i|n, j|n} gcd(i,j)$$ I can't find a way to solve this. Can I find a general formula or a way to solve this?
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### how to calculate double sum of GCD(i,j)?

I stumbled upon a programming question which wanted me to calculate : $$G(n) = \sum _{i=1}^{n} \sum _{j=i+1}^{n} gcd(i, j).$$ now I wrote a code to solve this problem but it takes polynomial time to ...
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### Big O for a $\cos$ series

I have to show that $\sum_1^N \cos(nx) = O(\frac 1{|x|}), [-\pi, \pi]$, x different from 0. I really don't know how to show that. I obviously know that $\cos(nx)$ is bounded by $1$, I know what ...
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### Proof $\sum_{k=1}^n \frac{1}{(k+1)^a}$ < $\frac{1}{a-1} - \frac{1}{(a-1)(n+1)^{a-1}}$

I also know that $\frac{1}{a-1} - \frac{1}{(a-1)(n+1)^{a-1}}$ = $\sum_{k=1}^n \frac{1}{(a-1)k^{a-1}} - \frac{1}{(a-1)(k+1)^{a-1}}$ Any hint or help to solve this please?
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### How to determine a formula for an index of compliancy

I hope you will be patient with the inarticulate question of a non-mathematician. It's hard to get an answer when you don't even know how to ask the question. Here the contest: Let's say that I have ...
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### How to compute $\lim\limits_{x\to 0}\frac{e^{x^2}-\cos{(2x)}-3x^2}{x^2\sin{x^2}}$ limits by using taylor series?

How to compute $\lim\limits_{x\to 0}\frac{e^{x^2}-\cos{(2x)}-3x^2}{x^2\sin{x^2}}$ limits by using taylor series? I think that we need to take every familiar taylor series (i.e. $e^x,\sin{x}$) and ...