# Questions tagged [summation]

Questions using the Sum command, especially for series and other algebraic objects, and related functions such as SumConvergence

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### How to differentiate formally?

I have been wrapping my head around this for a while now and I have not found a solution so far. I want to work with an arbitrary number of variables in Mathematica and use some built in functions. To ...
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### Double series over primes

I'm very curious if the following double series over primes has a closed form: $$\sum_{k \in \mathcal{P}}\sum_{n \in \mathcal{P}}\frac{1}{k\;n(k+n)^2}$$ where $\mathcal{P}$ denotes the set of all ...
• 1,415
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### Ways to compute inner products of tensors

One way to evaluate the following sums is combining Table and Sum: $u_{abcd} = \sum_{e=1}^3 v_{aeb}w_{ced}$ $q_{ab} = \sum_{d,e=1}^3 v_{d e a}w_{deb}$ It will look like ...
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### Sudden increase in timing when summing over 250 entries

I see a sudden increase of Timing by a factor of thousands when I sum over 250 elements of a matrix rather than over 249. So for instance, this table contains sums ...
• 345
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### How to sum over a List

list = {11.5575, 11.397, 5.52734, 4.0878, 2.54815, 1.86652, 2.55028, 2.14952, 1.6242, 1.34117} I have a list of numbers. How do I make a function that creates a ...
• 2,264
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### Sum or Product with Exclusions

Is there a built-in feature for handling things like: $$\sum_{\substack{i=0\\i\ne j}}^n\frac{a-a_i}{a_i-a_j}$$ and $$\prod_{\substack{i=0\\i\ne j}}^n\frac{a-a_i}{a_i-a_j}$$ or should I work out some ...
• 884
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### Error computing sum of sum of digits

I've defined a function that computes the sum of the base-b digits of n: DigitSum[n_, b_] := Total[IntegerDigits[n, b]] Then I defined a function that computes ...
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### Sum not recognized as a linear operator by Solve

When I try to solve an equation with a constant under the summation sign, Mathematica does not factor the constant out of the summation and fails to solve a simple equation. How do I make Mathematica ...
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### SumConvergence difficulty

Backslide introduced in 9, persisting through 11.2. Consider the series $\sum_{n=1}^\infty\sin\frac{50}{n^2}$. The terms are eventually positive. ...
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### How can I speed up this code with multiple sum？

There are 4 variables in this multiple sum, therefore it may take a long time. I have run this program for 12 hours, but no result untill now. I want to know how to speed up this code. Any help or ...
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### Why does Mathematica think this series doesn't converge?

Bug introduced in 10.0 and fixed in 11.1 (reported as CASE:3790525) Here's a simple series: Sum[t^k DiscreteDelta[k]/k!,{k,0,Infinity}] Mathematica says that ...
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### SumConvergence[((-1)^n)/(Sqrt[n] + (-1)^n), n] returns True in Version 10.2?

Bug introduced in 10.4.1 or earlier and fixed in 11.0.0 I claim that the series $\sum_{n=2}^{\infty}\frac{(-1)^n}{\sqrt{n}+(-1)^n}$ diverges. To see this, rewrite the $n^{th}$ term as follows: \begin{...
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### How can we simplify equivalent sums over different index variables?

The following should be True for any function x: ...
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### Find asymptotics of $\sum\limits_{i=0}^{n/3} 2^i \binom{n-i-1}{\frac{2n}{3}-1}$

I have an expression 2^n / Sum[ 2^i Binomial[ n - i - 1, 2n/3 - 1], { i, 0, n/3}] ...
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### define variable index

im in the medal of coding and i reached the point where i have something like this, the problem is i have up to 35 terms and all should be index in order to preform summation to count all ...
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### How to exclude numbers in a series and still plot the graph? [duplicate]

I want to plot this: $\displaystyle\sum_{n=-{10}\atop n\ne \pm 1}^{10} \dfrac {4i(-1)^{n}n}{(n^2 - 1)^2}e^{inx}$ but have no idea how I can exclude the cases for when $n = \pm 1$. I don't wish to ...
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### Slow Sum with Subscripts

Edit: My original question implicated D in the problem, but it seems unrelated, so I've removed that part of the question. I am writing a function that uses ...
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1 vote
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### Strange evaluation of an sum involving binomial coefficients

I stumbled upon this problem while playing with Mathematica 10. Can anyone help me explain the following behaviour? I define a sum ...
1 vote
654 views

### Constraint on variables in summation

Is it possible to have a constraint on variables in summation of series just similar to pattern constraint e.g. ...
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1 vote
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### Why is the function assuming not taken in consideration?

In the following code, I assume that my variables are strictly positive. However, mathematica doesn't take this in consideration when it evaluates the If : the If is still in a non simplified form. ...
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1 vote
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### Creating my own midpoint rule function in Mathematica

I'm building my own function that is basically a midpoint riemann sum, but I cannot seem to get it to work. Currently I have ...
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1 vote
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### Manipulating infinite series

If I type Sum[f[x],{x,m,Infinity}]-Sum[f[x],{x,m+3,Infinity}] I would like Mathematica to return something like ...
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