# Tagged Questions

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

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### plotting summation to check for convergence

Our assignment was to enter in a series and check to see if it converges by graphing. However, when I attempt to graph it, I get a bunch of errors that I'm not sure what they mean. Best way to show ...
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### What is the underlying algorithm to simplify sums of reciprocals of polynomials?

Flipping through Wolfram's blog entry on Leibniz, W noted Huygens' interview test for the young Leibniz, namely to determine: $$\sum_{n\ge2} \frac{1}{{n \choose 2}}$$ It's one thing to do this by ...
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### Extract coefficients from sum

I would like to extract coefficients of indexed variables from a large sum. The following is an example motivated by linear regression to illustrate the problem. Consider the (unnormalised) log ...
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### Sum of a set of elements in a array?

For a function I do this (Integrate over circular range): NIntegrate[x*y Boole[Sqrt[x^2 + y^2] < 3], {x, 1, 5}, {y, 1, 5}] ...
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### Why this upvalue doesn't escape from Sum?

Probably a hard question, but I decide to cry out loud :). This is actually another problem I encountered when answering this question. Consider the following transform rule stored as an upvalue: <...
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### tabulating summation series with restrictions

Trying to solve this question for a good 5 hours but remained stuck. My intuition tells me I am missing something trivial that I've overlooked or forgotten. I am restricted only to the function 'table'...
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### Getting $e$ closer than $0,001$?

Everyone knows that $\sum \frac{1}{n!} =e$. How should I make a program in Wolfram Mathematica, that tells me, how many members I need from the sum, to get a number, with mistake smaller, than $0,001?$...
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### Infinite sum not evaluated unless split into even and odd terms

This sum s = Sum[Gamma[k/2]/(2 k!), {k, 1, ∞}] $\sum _{k=1}^{\infty } \frac{\Gamma \left(\frac{k}{2}\right)}{2 k!}$ is returned unevaluated (version 10.1.0). ...
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### Sum of operations involving an arbitrary number of 2D vectors

I need to define an equation stating that the sum of n operations involving n 2D vectors and ...
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### Wrong output from Mathematica when evaluating a summation

Consider the sum $$\sum_{r=0}^n \binom{n-r-1}{n-r}$$ This sum is not zero because when $r=n$, the result is $\binom{-1}{0} = 1$. However, plugging this formula into Wolfram Alpha does return zero. ...
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### Anyway to speed up my plot of two lines?

My code takes very long time to plot these two lines. But it is very quick when I use Integrate instead of Sum in the formulation. But the there is a constant difference between using Integrate and ...
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### Problem with simplification KroneckerDelta

Bug introduced in 8.0 or earlier and fixed in 9.0 I have: ...
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### Follow-up to “How to differentiate formally?”: Efficiency concern

In link to "how to differentiate formally?" and particularly to the answer by @Jens, I want to do something like this: ...
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### Relevant help page for: Sum?

When I type Sum into Mathematica, it also offers Sum in the autocomplete dropdown, but when I click the little menu button next ...
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### evaluation of the sum of KroneckerDelta

I need help. I need to know why the next code doesn't simplify in Mathematica 10 but it does in Mathematica 8. I need some similar in version 10. What can I do? ...
180 views

### How do I solve for a variable inside a sum but independent of the summation index?

How would I go about solving the following for c? Solve[0 == Sum[(t[i]*m[i] - c*t[i]^2)/s[i]^2, {i, 1, n}], c, Reals] I get ...
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### Solve equation with sum in it

Have trouble to solve this equation. Anybody knows where're the problems? ...
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### Follow up: how to evaluate this double sum quickly

This question is a follow-up to my previous question. The code I use at the moment is the following: ...
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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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### symbolic summation involving kronecker delta

I have to perform symbolically summations of this kind $\sum_{ijkl} V_{ijkl} c_i c_j c_k \delta_{l,m}$ where $V_{ijkl}$ are quantities which depend on 4 indices and $\delta_{l,m}$ is the kronecker ...
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### Programming a MaxMin Linear Optimization

I want to program a function for a two-player game. Basically it's like this: . Each player has an array of options, and the result of the game is based on both players choices. So heres my most ...
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### Why does this simple sum function fail to compile?

Consider the following compiled function, which takes a $12 \times 5$ array $x_{ij}$ of real numbers and computes the triple sum $$\sum_{k=1}^5 \sum_{i=1}^{12} \sum_{j=i+1}^{12} x_{ik} x_{jk}.$$ <...
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### Bug in splitting sum

I was trying to evaluate the following sum. $$\frac{2}{m}\sum_{\substack{\text{odd }k\\1\leq k\leq m-1}} f(\frac{m+2+\sqrt{m^2-4k+4}}{2})+f(\frac{m+2-\sqrt{m^2-4k+4}}{2}).$$ And I wrote the ...
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### Is there an easy way to speed up this double summation in Mathematica

I would like to make an intensity plot of Bosons in a harmonic trapping potential. Hence, I would like to execute the following double summation (everything made dimensionless) for as many terms as ...
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### Problem with precision of fraction numbers

I have tried to take a series of harmonic numbers using Mathematica and its precision but there has been an issue. So far when I computed the sums at a whole numbers using a precision of 100 digits I ...
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### Problem with calculating Harmonic Numbers

I have tried to take a series of Harmonic Numbers using mathematica but there have been issues in calculations. So far when I computed the sums at a small value range such as ...
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### Plotting a partial sum (Fourier Series) [closed]

This is what I'd like to plot: ...
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### How to make x^0 be 1 as x->0 in a power series?

I'm trying to so this: s[x_] := Sum[a[j]*Sum[a[k]*k*x^(k - 1), {k, 1, Infinity}]^j, {j, 1, Infinity}]; s[0] It returns a 0^0 indeterminacy warning. But a human ...
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### Plotting a Taylor series of Partial sum

Hi people, I want to plot the partial sum from n=0 to n =6 with the given function f about the point a=0 (just the maclaurin series). Unfortunately, I am unable to make sense of the issue M'tica is ...
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### Is this a bug of NSum?

Check this: NSum[Log[Abs[m]],{m,1,24}] (*54.7847*) NSum[Log[Abs[m]],{m,1,25}] NSum::nsnum: Summand (or its derivative) (Abs^[Prime])[m]/Abs[m] is not ...
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### WorkingPrecision in a sum

If I am interested in getting a fairly precise plot of f2 below, can I use WorkingPrecision to do this? ...
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### Multiple Constrained Sum

I need to perform a multiple summation, that obeys some conditions. This arises in the study of a statistical physics model. q=Exp[-β]. I would like to ask if ...
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### Sum of hypergeometric functions, variable number of arguments

How can I write in Mathematica an expression like this? $$\sum_{k=1}^n {_{k}F_{k}} (1,1,\dots,1; \,2,2,\dots,2; \,z) ~,$$ where ${_{p}F_{q}}$ is the generalized hypergeometric function. My problem ...
250 views

### Fastest way to sum the upper triangle

I feel like this is an recurring question: if there's a symmetric matrix whose diagonal is not all 0, how could I get the sum of the part of it that's above the diagonal as fast as possible? Small ...
101 views

### What can I use as an equivalent of python zip in mathematica inside of Sum[]? [closed]

I want to take two lists of the same length: widths and weights, and sum a function (of 3 variables) over a single index using the elements from both lists that have that index. Then I want to plot ...
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### The fastest way of raising indices of high rank tensor

I have some high dimensional high rank tensors, let's say $$F_{ijkl}$$ and I need to find $$F^{abcd}=g^{ai}g^{bj}g^{ck}g^{dl}F_{ijkl}.$$ Here $g^{ij}$ is the contravariant metric. Simple summation ...
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### How should I enter indexed terms? For example, constants $n_k$ for $k\in\{1,\,\ldots,\,N\}$

How should I enter $\quad \quad \sum^{N}_{k=0}{f(n_k)}$ into Mathematica? More generally, how should I work with the indices? Take the following as an example. I know how the ...
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### Simplify a huge expression with limited memory

I would like to perform some analytical sums such as the following ...
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### How can I get the exact value of this infinite series? [duplicate]

I want to compute the exact value of this infinite series $$\sum_{n=1}^\infty\arcsin{\left(\dfrac{2}{\sqrt{n(n+1)}(\sqrt{n}+\sqrt{n-1})}\right)}$$ I tried to implement something like this ...
What is a way to nest a product in a sum: $$\sum_{i=2}^{N}\cos\theta_i\cos\theta_i^\prime\prod_{j=i+1}^{M}\sin\theta_j\theta_j^\prime$$ where $N$ and $M$ are two numbers? Thank you.