# Questions tagged [summation]

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

11,296 questions
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### If $x^n-3x^{n-1}+2x+1=0$, compute $\sum_{k=1}^n \frac{x_k}{x_k-1}$ [closed]

Let $x_1, x_2, \ldots, x_n$ be the $n$ roots of the equation $x^n-3x^{n-1}+2x+1=0$. Calculate the sum $\sum_{k=1}^n \frac{x_k}{x_k-1}$. Can somebody give me some tips, please? It's pretty hard to ...
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### Check of $f(x)=\sum_{n=1}^{\infty}\frac{1}{x^2+n^2}$ properties

For function defined as $$f(x)=\sum_{n=1}^{\infty}\frac{1}{x^2+n^2}$$ check if $f$ is continuous and differentiable function. My approach: I would like to use the connection between this sum and ...
1answer
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### Value of a binomial series

Some time ago a question was asked here regarding the value of the sum $$\sum_{i=0}^k \frac{{2i \choose i}}{4^i}$$. But it was deleted later by the OP.I went around it but didn't find a solution. ...
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### What are the elements of a fractional summation?

For example, what are the elements in: $$\sum_{i=0}^{2.5} i$$ Background: As part of a program I wanted to generate a sequence along $i^2$ in a range $[a,b]$ with a given sum $c$. So, \begin{align}...
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### Proof idea for sum of square / square of sum inequality

This problem came up in a long proof and it is not clear to me how to show this. I tried to apply Cauchy-Schwarz but it is not tight enough. Any idea? Let $\Delta$ be a matrix of real values with $B$ ...
1answer
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### A curious summation question from pre-RMO 2016

This problem came in the Pre-RMO (Regional Mathematics Olympiad) - Delhi Region (INDIA). I've been solving these questions, and this particular summation question is proving to be quite difficult. ...
2answers
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### Is there a sum of “n+j” terms equivalent to n!

Is there any function so that... $$\sum_{k=0}^{n} f(k) = n!$$ or, $$\sum_{k=0}^{n+j} f(k) = n!$$ where j is any arbitrary integer?
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### Calculate ssgsea score by hand

I hope this is the right place for this question, if not, feel free to suggest more suitable sites. I would like to calculate a single sample gene set enrichment analysis (ssGSEA) score step by step ...
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### Sum consecutive tuples [on hold]

I have a set of tuples that can be consecutive based on the last element, like so: (1,2),(2,4),(4,3),(3,2) How can I make the sum of the values without counting the consecutive elements twice and ...
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### The Lagrange Interpolation formula – Spivak's Calculus Ch 3 Problem 7(b)

The problem: Now find a polynomial function $f$ of degree $n - 1$ such that $f(x_i) = a_i$, where $a, \ldots, a_n$ are given numbers. I found that this question had been asked before, but I did not ...
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