# Tagged Questions

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

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### Infinite Sum - Result not correct for all cases?

Evaluating the Sum Sum[a^i, {i, ∞}] yields -(a/(-1 + a)) which obviously only holds ...
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### Finding a closed form solution [migrated]

For the sequence 0 2 8 34 144 ... The recurrence relation is: \begin{align*} E(n) = 4*E(n-1)+E(n-2) \end{align*} How to calculate the closed form expression ...
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### Why does Mathematica return Indeterminate for this converging infinite sum?

Limit[Sum[k/(n^2 - k + 1), {k, 1, n}], n -> Infinity] This should converge to 1/2, but ...
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### Infinite summation with absolute value

Recently I need to compute the summation like the following form: Sum[t^Abs[n - m], {n, -∞, ∞}, Assumptions -> m ∈ Integers] But Mathematica cannot figure it ...
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### Error “Summand (or its derivative)…is not numerical at point m = -85.” on a simple sum

I'm a beginner on mathematica.. I'm trying to calculate a simple sum of a function, ...
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### Error with Parallel Calculation on Large Multiple Sums [closed]

I am attempting to complete the following quadruple sum: ...
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### Evaluating summations involving Fibonacci numbers in terms of Fibonacci numbers

There are many summations involving Fibonacci numbers which Mathematica 10.4 is able to evaluate directly in terms of Fibonacci numbers. For example, Mathematica evaluates the summation given below as ...
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### Simplify results further

I have an extremely long result in polynomial form following some matrix operations. However, given the symmetry of the problem, I can safely say that the solution will reduce much further than is ...
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### How can I evaluate a certain kind of summation?

I have the following sum P0, P1 and P2 are constants. The problem is to assign all ...
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### Symbolic series

Mathematica realises, of course, how to deal with symbolic series: Sum[g[x]^k, {k, 0, ∞}] (*Out: 1/(1 - g[x]) *) I.e. it does not worry about values of ...
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### How to sum over half integers? [closed]

I have an expression of the form Sum[1 + x^n + x^(n^2/2), {n, 0, 10}] but I want to sum over half integers, that is, I require that $n \in \mathbb{Z}+\frac{1}{2}$ ...
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### RootSum result manipulation/simplification

Consider the sum sum1 = Sum[ k/( k^7 - 2 k + 3), {k, Infinity}] ...
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### sums over partitions and sums with variable indices

Is there neat way to implement following sums in mathematica? $$s(l,k)=\sum\limits_{p_1+p_2+...+p_l=k} f_l(p_1,p_2,...,p_l)$$ and $$t(l)=\sum\limits_{i_1,i_2,...,i_l=1}^n f_l(i_1,i_2,...,i_l)$$ Where ...
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### Double Sum Involving Condition

I would like to compute the dimensions of some small free nilpotent Lie algebras. However, I am totally new to this and I could not figure out how to write the double sum which gives the dimension of ...
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### Calculating sum of BesselJ[n, x]

My friend has a sum in his research paper that looks like this $$\sum_{n=-\infty}^{\infty}\frac{J_n^2(x)}{n-\kappa}.$$ He was able to calculate this sum analytically, by substituting the denominator ...
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### How to correctly implement in a new function the scoping behavior of Table, Sum and other commands that use Block to localize iterators?

It is documented that "Block is automatically used to localize values of iterators in iteration constructs such as Do, Sum, and Table." Therefore the dummy index (iterator) in a Sum is shielded ...
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### Can a single Sum with multiple iterators be different from nested Sums?

Multiple sums are documented with two or more iterators, for example: Sum[1/(j^2 (i + 1)^2), {i, 1, Infinity}, {j, 1, i}] however the same answer can be ...
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### Accessing the elements in a table is slower than calculating each time?

This is a follow-up of How to accelerate combinations and sum calculations here? I have tried all tricks but when N reaches 35 the time is still intimidating in a 16-core server, which is far better ...
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### Creating a non-zeta-ified sum

The expression Sum[i^(-s), {i, 1, ∞}] evaluates to Zeta[s] But, of course, this is not strictly correct as ...
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### Symbolic sum of Stirling numbers gives wrong answer

Bug introduced in 9.0.1 or earlier and fixed in 10.4.1 This issue originated from my attempt to answer a question on MathOverflow: ...
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### How to accelerate combinations and sum calculations here?

I have a 4d matrix H defined as below (embedded with combinations and sums) ...
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### How do I add the nth element for every line in a text file?

Suppose I have a text file, in this format: ...
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### Partial Sum of Binary Sequence not Working

I have the following code: ...
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### Problem of Summation

I want to calculate something like this: $$w_t = \sum_{i+j=t}c_{5-i,4-j}.$$ for $t=0,1\cdots8$. How I can write the code? I assume that $i$, $j$ and $t$ are all positive integers. Thank you very ...
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### Expand series unevaluated

I'm newbie in Mathematica. I'd like to obtain nice and verbose output for any series calculation. For example, given a simple sequence n*(-1)^(n-1) and ...
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### DifferenceRoot question

I was doing the following sum: $$\sum_{i=2}^k \frac{(-1)^i}{i-1} \binom{2k-i-1}{k-1}x^i$$ First, Mathematica simplifies it to some DifferenceRoot function: ...
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### $\sum_{k=1}^{\infty }\left\lfloor\frac{5}{5^k}\right\rfloor$ giving wrong answer?

Bug introduced in 7.0 or earlier and persisting through 10.4 or later When I try to evaluate the following: $$\sum_{k=1}^{\infty }\Bigg\lfloor\frac{5}{5^k}\Bigg\rfloor$$ using ...
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### Wolfram Mathematica: Sum of a function over a list [duplicate]

I have the function: $I_q(n)=\frac{1}{n}\sum_{d|n}\mu(d)q^{n/d}$, where $\mu(d)$ is the Möbius function. How do I get it in Wolfram Mathematica? It should be something like that: ...
The input Sum[d^t,{t,0,Infinity}] produces output 1/(1-d) which is correct for $|d|<1$. But for $|d|\geq1$ the sum does ...
How do i merge these 3 function onto 1 set of function to plot? Construct the series representation of a function $f(x)$ using up to $N0$ terms: ...