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

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5
votes
3answers
143 views

incorrect exact sum of a series

Sum[(-1)^m*(1/Binomial[2*m + 2, 2] + 1/Binomial[2*m + 3, 2]), {m, 0, Infinity}] gives the right value -2 + π but the same ...
1
vote
2answers
85 views

Engel expansion

How do I do an Engel expansion in Mathematica? And find the unique non-decreasing sequence of positive integers $ \{ a_1 ,a_2,a_3,\dots \}$ , such $$\frac{e}{\pi}=\frac{1}{a_1}+\frac{1}{a_1 a_2}+\...
5
votes
3answers
240 views

Make a vector of sums of matrix rows

I have a matrix in Mathematica: ...
0
votes
0answers
21 views

Adding a list up to a starting value [duplicate]

The code that i need has a starting value of 5. From this starting value on a list of numbers is added consecutively like this list {-0.1,-0,3,-0.1,0.1,-0.1} ...
4
votes
2answers
62 views

Controlling evaluation in a custom summation function

I'm doing some computations that involve summations with many indices over the same range - consider the simplified example Sum[a[i,j],{i,1,2},{j,1,2}]. To prettify ...
4
votes
1answer
144 views

How to increase the evaluation speed of this somewhat complicated table / matrix operation?

I'd like to calculate the following one-dimensional array: OneDimArray = Table[(Norm[Sum[ MatrixA[[i,j]]VectorB[[j]],{j,N}]])^2,{i,N}] However this takes a very ...
2
votes
1answer
79 views

Constrained Sum evaluation [duplicate]

I need to sum up F[x1,x2,...] over x1,x2,... where I have a constraint: x1+x2+...=n (n=positive integer number). For example, I have F[x1,x2] and x1+x2=3, so for the sum I get F[3,0] + F[2,1] + F[1,2] ...
33
votes
2answers
613 views

$\sum_{k=1}^{\infty }\left\lfloor\frac{5}{5^k}\right\rfloor$ 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 ...
0
votes
2answers
84 views

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 ...
6
votes
0answers
75 views

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 ...
0
votes
0answers
58 views

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 ...
1
vote
2answers
81 views

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}] ...
5
votes
2answers
172 views

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: <...
2
votes
5answers
79 views

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'...
1
vote
0answers
48 views
1
vote
5answers
191 views

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 $0,001?$...
5
votes
2answers
92 views

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). ...
2
votes
1answer
51 views

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 ...
6
votes
2answers
110 views

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. ...
2
votes
1answer
105 views

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 ...
9
votes
1answer
83 views

Problem with simplification KroneckerDelta

Bug introduced in 8.0 or earlier and fixed in 9.0 I have: ...
2
votes
0answers
61 views

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: ...
6
votes
1answer
107 views

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 ...
8
votes
1answer
118 views

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? ...
3
votes
2answers
194 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 ...
0
votes
1answer
101 views

Solve equation with sum in it

Have trouble to solve this equation. Anybody knows where're the problems? ...
0
votes
1answer
133 views

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: ...
14
votes
3answers
284 views

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: ...
4
votes
2answers
194 views

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 ...
3
votes
1answer
130 views

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 ...
7
votes
1answer
176 views

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 $$ \sum_{k=1}^5 \sum_{i=1}^{12} \sum_{j=i+1}^{12} x_{ik} x_{jk}. $$ <...
6
votes
2answers
382 views

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 ...
6
votes
1answer
264 views

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 ...
0
votes
1answer
60 views

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 ...
1
vote
0answers
74 views

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 ...
0
votes
1answer
98 views

Plotting a partial sum (Fourier Series) [closed]

This is what I'd like to plot: ...
3
votes
1answer
76 views

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 ...
1
vote
1answer
223 views

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 ...
4
votes
1answer
242 views

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 ...
3
votes
1answer
79 views

WorkingPrecision in a sum

If I am interested in getting a fairly precise plot of f2 below, can I use WorkingPrecision to do this? ...
4
votes
0answers
108 views

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 ...
2
votes
1answer
119 views

Plotting a partial sum

I am given the Legendre expansion of the first kind. $$f(x)=\sum_{n=0}^{\infty}A_{n}P_{n}(x).$$ I have worked the coefficient to be $$A_{n}=\frac{1}{\left \| P_{n}(x) \right \|^{2}} \int_{x=-1}^{x=1}...
3
votes
1answer
138 views

Calculate sum of probabilities in multinomial model

The question at hand: On average in every 7th chocoloate egg there is a figure to be drawn from a known list of special figures (e.g 15 distinct pieces) the other draws are on average fails. With ...
3
votes
2answers
123 views

How to deduce the Ramanujan's summation of this series?

I have already asked a similar question about Ramanujan's summation in general but received no good answers. Now I am interested in this exact series: $$\sum _{n\ge1}^\Re (24 n + 12 n^2)$$
3
votes
1answer
108 views

Range of summation in simple Plot seems off

I was trying to reproduce a picture in a book by Havil of the sum, $$s = \sum_{r=1}^{\infty}\frac{\mu(r)}{r}\left(Li(x^{\rho_k/r})+Li(x^{\rho_k*/r})\right) $$ using ...
1
vote
1answer
112 views

How to simplify the equation and speed up the codes for four 100*100 matrices

I have to make a sum over 4 variables. Each variable corresponds to a 100*100 matrix. I want to know how to speed up this code. This problem is related to the previous problem 1 and 2. But now I need ...
1
vote
2answers
101 views

How can I speed up this code with 4 variables sum

I have to make a sum over 4 variables. My code is very very slow. I want to know how to speed up this code. This problem is related to but different from one previous problem. Any help or suggestion ...
4
votes
4answers
268 views

How to stop a summation when a variable is small enough?

I meet with a problem. I hope to get an infinite summation of $f1(x)/f2(x)$ which converges to zero. So my code is Sum[f1[x]/f2[x],{x,Infinity}] or ...
4
votes
2answers
257 views

Determine the coefficient of expansion of the product of two sumations?

I would like to determine the coefficient of a desired term in the product of two summation where the powers of $x$ are not necessarily integers. For example $$ \sum_{i=1}^N x^{1/i}\sum_{j=1}^N x^{1/j}...
0
votes
1answer
57 views

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 ...