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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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0
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1answer
446 views

Why does the evaluation of this series fail?

The following series expression holds: ...
3
votes
2answers
169 views

Automatically generated summation region

In a multiple Sum I need to put an automatically generated summation region. But when I generate the summation region automatically I get a list whose elements are ...
7
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2answers
3k views

Can I define a function for vectors of arbitrary dimension?

Is it possible to do analytic calculations with Mathematica? For example, I want to compute: $$\partial \frac{\sum_{j=1}^n G_{j} \prod_{k=1}^{j-1} (1 - G_{k})}{\partial G_l}=-\prod_{k\neq l} (G_k-1)$$...
5
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2answers
3k views

Sum over all permutations

I have n variables and a function that has all of them as variables. n-3 of them in terms of the entries of two lists. The possible entries in the lists $\alpha$ and $\beta$ range from {2,...n-2}. Now ...
11
votes
6answers
528 views

Performing Computations on Sets

I would like to find a permutation of $\quad S=\{\frac{1}{10}, \frac{1}{2}, \frac{4}{7}, \frac{3}{5}, \frac{2}{3} \}\quad$ that maximizes the sum of theses elements raised to unique powers: $\;\{0,1,2,...
4
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3answers
1k views

Summation with constraints

I am trying to do the summation shown below, $\sum_{i_1=0}^{imax_1} \sum_{i_2=0}^{imax_2} \dots \sum_{i_k=0}^{imax_k} f(i_1,\dots,i_k)$ $k$ is a variable. Therefore $i$ and $imax$ are defined as ...
14
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1answer
283 views

Baffling increase in runtime

Background of my question I discovered Project Euler today, and decided I would work through the problems in Mathematica. I became obsessed with the first problem, which is essentially "sum all the ...
17
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2answers
15k views

How do you put conditions on indices in a sum?

I'm relatively inexperienced with mathematica, so I apologize if this is a trivial question. I want to take a double sum over a function $f(i,j)$ of two indices, of the form $$ \sum_{i = -\infty}^\...
4
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2answers
391 views

Numerical sum does not give consistent results

Consider the function ...
2
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2answers
170 views

The proper way to write the input for a certain series

Mathematica tells the series below doesn't converge. I think it converges. What would the proper way to write things be as an input? ...
5
votes
3answers
500 views

Why the difference?

When I do the double sum using the sigma notation I get $$1 + \sum_{n=0}^{\infty}\sum_{k = n}^{\infty} \frac{1}{(k+2)k!}$$ $1 + e - \cosh[1]$ When I do the sums as below, I get the expected ...
11
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5answers
10k views

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 ...
5
votes
2answers
194 views

Speed up plot of $\sum_{j\ge1} 2^{-j}(1-2^{-j})^{n-1}$

I'm a beginner at Mathematica. I would like to plot the following function: $${n\over2} \sum_{j\ge1} 2^{-j}(1-2^{-j})^{n-1}$$ However the following code is just too slow: ...
-5
votes
1answer
394 views

plotting an equation with double summations

Thank you so much for the helpful comments. Now able to manage to plot all the functions. ...
3
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1answer
1k views

Sum and NSum gives different solutions

I'm working on a Mathematica lab for Calc. 2, and I ran into a problem last night. I was trying to calculate the midpoint approximation of the definite integral of ...
3
votes
1answer
208 views

Can we give Mathematica hints for symbolic sums and products?

I have this question at MO and I would like to know if we can give hints to get the symbolic sums and products to come out as $\frac{6}{\pi^{2}}\pm\epsilon$ instead of $0.60792710...$ accurate to $\...
3
votes
1answer
342 views

Sum of positive terms gives negative answer

Bug introduced in 7.0 and fixed in 9.0 Mathematica evaluates Sum[((n - y - 1)*(n - y)^2*n^y)/y!, {y, 0, n - 2}] as -2 e^n n. ...
5
votes
1answer
499 views

Problem with creating a large list of tuples

This is a follow-up question from Sum of Multinomial Coefficients I have thought about the meaning of the formula I mentioned and, with help, I implemented the following code: ...
3
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3answers
1k views

Sum of Multinomial Coefficients

Basically, I want to write a function to compute the following sum $f(m,L):=\sum_{0\leq k_1,\cdots, k_n\leq m} \binom{m}{k_1,k_2,\cdots k_n}$ and $\mathrm{supp}(k)=L \subseteq \left \{ 1,...,n \right ...
3
votes
1answer
752 views

Summation of If statements

The following made me curious. Suppose you want to sum the if statement If[x[i] < 1., x[i]^2, 0.] over i=1,2, i.e. ...
5
votes
1answer
313 views

Summing tensors in mathematica

How do I perform the following summation in mathematica? \begin{equation} \Sigma_{m=1}^5 e_{ijklm}A^{mn} \end{equation} I have the $e_{ijklm}$ tensor of rank 5 in 5 dimension as a array and $A^{mn}$ ...
3
votes
3answers
899 views

Efficiently compute double sum

Is there a "Mathematica Way", like Map or Apply to compute the following double sum? $\sum_{i=1}^{N_1}\sum_{j=1}^{N_2} m_i n_j \, f(\tau_{i} \gamma_{j})$ I have already stored the lists $m,n,\tau,\...
1
vote
2answers
719 views

Adding multiple Complex Numbers in Euler form

Say I have a series of $n$ complex numbers of the form $A_k e^{(I \ \theta_k x)} $ where $A_k$ is a real number and so is $\theta_k$ and $k$ runs from $1$ to $n$. $x$ is an algebraic symbol. ...
2
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1answer
197 views

How to evaluate the sum over a hyperplane

I have difficulties in evaluating the following expression: $$\sum_{\small n_1+...+n_{k}=m-k}\; \prod_{i=1}^{k}\frac{1}{(n_i+1)(n_i+2)}$$ I have tried the function ...
5
votes
1answer
268 views

A triple sum related question

I'm trying to compute the triple sum Sum[ 1/(i! j! k! ), {i, 1, Infinity}, {j, i + 1, Infinity}, {k, j + 1, Infinity}] but Mathematica doesn't return any value. ...
3
votes
1answer
1k views

Nested Sums to multiple sum

I would like to automatically "move nested sums to the left". I mean, just take out of an expression all the summations and go from a nested Sum to a multiple sum. Something like starting with: ...
17
votes
5answers
3k views

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 ...
4
votes
2answers
283 views

What causes this strange convergent sum?

N[Sum[1/(x^2 + 1), {x, 1, Infinity}], 5] N[Sum[1/(x^2 + x + 1), {x, 1, Infinity}], 5] 1.0767 0.79815 + 0.*10^-6 I What causes the strange number?
7
votes
3answers
353 views

How to calculate this sum?

I want to find the sum $$S=f\left(\dfrac{1}{2012} \right) +f\left(\dfrac{2}{2012} \right) +\cdots + f\left(\dfrac{2011}{2012} \right), $$ where $$f(x) = \dfrac{4^x}{4^x + 2}.$$ I tried ...
3
votes
1answer
577 views

Mathematica 9 and later behavior with derivative of a sum

Bug introduced in 9.0 or earlier and fixed in 11.0.0 In: D[Sum[Sin[x],x],x] D[Sum[f[x],x],x] Out: 1/2 Cos[1/2 (-1 - Pi + 2 x)] Csc[1/2] 0 Function f is ...
36
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7answers
4k views

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 ...
5
votes
1answer
1k views

Showing the terms in a partial sum?

I am trying to get s[n_]:=Sum[1/2^k,{k,1,n}] to show me the actual terms involved in the $n$th partial sum and not just the sum itself. I've tried ...
9
votes
2answers
702 views

RootSum result manipulation/simplification

Consider the sum sum1 = Sum[ k/( k^7 - 2 k + 3), {k, Infinity}] ...
19
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2answers
5k views

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 ...
4
votes
2answers
550 views

Indeterminate expression. Where?

Consider the following: ...