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

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2
votes
2answers
306 views

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 ...
1
vote
2answers
72 views

Double sum in mathematica

It may look like a stupid question, but I was really confused by how double sums works in mathematica: After simplification, the function actually has nothing to do with n2? Also, when I manually ...
2
votes
0answers
49 views

Why can Mathematica compute numerical sums more efficiently when they are written as matrix operations?

Let $f(n)$ and $K(n,m)$ be functions such that the double sum, which we wish to evaluate numerically, $$ \sum_{n=1}^a \sum_{m=1}^a f(n) f(m) K(n,m) $$ exists when $a$ is some large positive number. I ...
4
votes
2answers
534 views

Simplifying expressions involving Sum

I am trying to use Mathematica to simplify a symbolic expression involving Sum. The expression is defined as follows: ...
0
votes
0answers
4 views

How to calculate a sum using a geometric series [migrated]

How to calculate this with a simple calculator. sum_{i=20}^n=59 0.1*600*1.04^(60-i) = ? I tried this but it's wrong. Can somebody please tell me where I made a ...
8
votes
1answer
121 views

SumConvergence[((-1)^n)/(Sqrt[n] + (-1)^n), n] returns True in Version 10.2?

Bug persisting through 10.4.1 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{equation*} ...
0
votes
1answer
38 views

Sums with index expressions instead of variables

Often I replace $k$ with, say, $m-k^2$ in a sum, obtaining something like this: $$\sum_{0\leq m-k^2\leq n} f(k)$$ Is there a way to input these without manually solving the inequalities?
3
votes
1answer
93 views

Speed up computation of sum from large matrix

I have a 3x3 matrix (252^3) of data (densities) and I want to compute a correlation xi from nearest neighbours as well as a sum involving a check whether the density is in a certain bin. The ...
1
vote
0answers
54 views

Assumptions aren't working in this sum

I have a sum that should be real: FullSimplify@Sum[1/(α n^4 + β), {n, 1, ∞}, Assumptions -> α > 0 && β > 0] But the result have involved even ...
4
votes
1answer
81 views

double sum with condition

I was trying to compute the following sum: $$\phi(x,y)=\frac{1}{4\pi^2}\sum_{(n,m)\neq(0,0)}\frac{1}{n^2+m^2}\exp(i(nx+my))$$ where the range of indices is, say, $-10\leq n, \,m\leq 10$. But I don't ...
7
votes
1answer
278 views

Differing answers when comparing Wolfram Alpha and Mathematica v.10.2

Out of curiousity, please consider following expression: Sum[(-1)^(n + 1)/n, {n, 1, 100000}] When evaluated using Wolfram Alpha: Result: ...
0
votes
0answers
49 views

Sum of Infinite convergent series

I have a series as Sum[(x^1 - (x - 1)^1) (b^Log[(1 + (x))]), {x, 1, Infinity}] which is convergent when b=0.3 and ...
2
votes
2answers
51 views

Why does ExpandAll not work within a symbolic sum?

If I evaluate Sum[(x + Subscript[y, n])^2, n] + (y + z)^2 // ExpandAll then the expression within the Sum is not expanded, yet ...
3
votes
2answers
134 views

Summing matrix products

I need to compute a double sum over a weighted matrix product: $L[M]=\sum_{i,j}^{N}\Lambda[[i]]\;\omega[[i]].M.\omega^{\dagger}[[j]]$. $\Lambda$ is a list of with N complex values(weights) and ...
8
votes
3answers
175 views

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 ...
3
votes
2answers
85 views

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: ...
33
votes
3answers
600 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
0answers
34 views

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: ...
12
votes
3answers
336 views

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 ...
1
vote
1answer
118 views

Summing infinite series that converge only for some parameter values

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 ...
0
votes
1answer
52 views

combining function and plotting

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: ...
0
votes
2answers
73 views

Failed to use SetPrecision

I am calculating the below formula: $$ \text{ER2}(\alpha,\text{K},\text{q})\text{:=}1+\sum _{m=0}^{K-1} \binom{K+\alpha }{m} \sum _{r=0}^m \frac{(-1)^r \binom{m}{r}}{\left(\frac{1}{q}\right)^{\alpha ...
0
votes
0answers
29 views

Simplify expression?

Suppose I have expressions that involve terms like: p1.p1+p2.p2+p3.p3+p4.p4 p1, p2, p3, and p4 are all elements of an array: ...
2
votes
2answers
252 views

Sum with IntegerQ does not converge

Why does Mathematica return: Sum::div: Sum does not converge. >> when I input: ...
27
votes
5answers
2k 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. ...
5
votes
2answers
242 views

Speed-up the computation of this sum of small matrices

Given a matrix mat with a large number of rows (a few thousands) and a few columns (between 2 and 10), I'd like to compute the sum of the "small" matrices obtained ...
1
vote
1answer
103 views

Asymptotics of sum of binomials

I would like to find the asymptotics of Sum[Binomial[n,i]*1/i^((n+1)/2),{i,1,n}] I saw Find asymptotics of Sum[2^i*Binomial[n-i-1,2*n/3-1],{i,0,n/3}] but I ...
5
votes
2answers
119 views

Problem summing an infinite series

Calculating this sum on Mathematica 10.3 Sum[(-1)^(r - 1)/((a^2 + r^2)r), {r, 1, Infinity}] gives the answer ...
0
votes
1answer
70 views

Slow sum computation

I'm doing a simple OLS regression and I strikes my attention that this very simple computation takes several seconds to perform in Mathematica ...
1
vote
2answers
66 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 ...
0
votes
1answer
144 views

Plotting a Double Sum

I am attempting to plot a graph of a function that is the absolute value of the double sum of an exponential function, and I keep getting errors. Here is the code: ...
5
votes
3answers
139 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 ...
12
votes
7answers
682 views

Numerical evaluation of a sum

I am trying to compute numerically NSum[(-1)^n/n^3, {n, 1, Infinity}]. Of course, using first Sum would work here, but often ...
5
votes
3answers
223 views

sum involving binomial coefficient

To evaluate $ \sum_{\substack{\text{even }k\\ 2\leq k\leq m-2}} \binom{m-2}{k-1}(k-1) $, where $m$ is an even integer. Running the following in Mathematica 10.3.0 (October 9, 2015) ...
3
votes
1answer
87 views

Euler-Maclaurin summation

I want to compute asymptotic approximations to partial sum of harmonic series in Mathematica, using Euler-Maclaurin summation formula. ...
4
votes
2answers
171 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 ...
5
votes
3answers
231 views
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
61 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
106 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 ...
3
votes
1answer
531 views

Mathematica 9 and later behavior with derivative of a sum

Bug introduced in 9.0 or earlier and persisting through 10.3.0 or later ...
5
votes
2answers
163 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
1answer
66 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] ...
3
votes
1answer
301 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. ...
10
votes
1answer
143 views

Bug in GeneratingFunction?

Bug introduced in 7.0 and fixed in 9.0.0 According to the documentation GeneratingFunction[a[n],n,x]==Sum[a[n]x^n,{n,0,Infinity}] However, for $a_n=1/(n+2)$ I ...
0
votes
0answers
48 views

Summation with one limit as parameters within summation itself

I want to sum one series with summation limits in which the first one given is a function of the terms within the sum, for example: ...
7
votes
3answers
302 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 ...
5
votes
0answers
70 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
2answers
76 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 ...