# Questions tagged [summation-method]

Use for methods for constructing generalized sums of series, generalized limits of sequences, and values of improper integrals.

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### Does Ramanujan summation extend Abel summation?

I was under the impression that if a series is Abel summable, then it is Ramanujan summable to the same value, but when I answered this question and was asked this as a follow-up, I was unable to ...
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### Find the value of $\frac{1}{1}+\frac{1}{1+2}+\frac{1}{1+2+3}+\ldots + \frac{1}{1+2+3 +\ldots+2015}$

The question: Find the value of $$\frac{1}{1}+\frac{1}{1+2}+\frac{1}{1+2+3}+\ldots + \frac{1}{1+2+3 +\ldots +2015}$$ If this is a duplicate, then sorry - but I haven't been able to find this ...
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### Closed-form summation of $\sum_{i=1}^n i\frac{x^i}{i!}$

Is there any way to find the closed-form of this finite summation, knowing that x<1? It is part of a larger equation that I am trying to solve/simplify, which has proven to use a lot of theory that ...
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### Alternative way to write triple summation

I have expression as $$\sum_{l\in \phi}^{} \sum_{i=1}^{K} \sum_{m\in \phi \setminus l}^{} a(l,i) b(m,i) c(l,m,i)$$ where $m\in \phi \setminus l$ means excluding $l$. I would like to write this ...
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### Summation of series with factorial

enter image description here I tried breaking the terms into differences or finding a generalised term but did not get it right. Can someone please help me to proceed with this?
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### Compute the following expression $\Sigma {100}{k=1} [k*(-1)^k]$.

I honestly have no idea how to format this. Anyways, I did this so far using the properties listed in my notes. I am pretty sure it is wrong, and if it isn't, where would I go from here?
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### An oscillating series of real numbers which can be resummed to a complex value

Okay so here I go again studying summability theory I was wondering the following problem but first I'll state a few conventions: A series diverges if the partial sums tends to $\pm \infty$, ...
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### A Summability methods which sum the harmonic series

Studying summability theory I've come across many summation methods however by now I know only two not very interesting method which re-sums the harmonic series $\sum_{n=0}^\infty \frac 1{n+1}$ : the ...