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

0
votes
0answers
23 views

What is wrong with my calculation ?

Help ! I had a problem with Z[Tan] error Part miss part 5 or {{1,1,1,1}{1,1,1,1}{1,1,1,1}{1,1,1,1}} something like that so this my function
-1
votes
2answers
44 views

Please help me get the ratio of x to y [on hold]

I need the ratio of x to y in this equation: sum [n*(x/10)^n/10^(n-2)] == y from n=1 to ∞ Thank you!
3
votes
4answers
163 views

Conditional Summations

I am not a math major, but for a networking class, I am taking I am required to do summations for probability. I know the logic but I don't know the mathematical theory to make this work. Using ...
2
votes
1answer
35 views

Plot variations in geometric sum within prescribed range

I have a simple geometric sum: Sum[a^(j + 1), {j, 1, k}] which evaluates to (a^2*(-1 + a^k))/(-1 + a) ...
1
vote
1answer
36 views

Find closed form for roots of trig formula

I have the expression Sum[(2 j \[Pi] Sin[(2 j \[Pi] x)/(r + 1)])/(r + 1)^2, {j, 0, r}] == 0 I want to find the roots in terms of ...
4
votes
2answers
101 views

Cumulative total of columns in a matrix or table

I have the following: matrix1 = {{a, b, c, d}, {e, f, g, h}, {i, j, k, l}, {m, n, o, p}} (Note that it's the data that matters, not the fact it's defined as a ...
1
vote
1answer
36 views

Summing results of a table

I have a simple table: example1 = Table[N[x^(x/r), 5], {r, 1, 10}, {x, 1, 10}] I want to create a new table ...
2
votes
2answers
55 views

How can I get the simplest result of this sum?

I am trying to find the sum $$\sum _{k=1}^n \frac{k+1}{(k-1)!+k!+(k+1)! }.$$ I tried Simplify[Sum[(k + 1)/(( k - 1)! + k! + (k + 1)!), {k, 1, n}]] and got ...
-1
votes
0answers
52 views

Summing a series [migrated]

How would I go about finding the sum of an alternating series that consist of 1 -1/2 + 1/3 -1/4 + 1/5... to the 8th term using a mathematical formula or is there no formula I can use
1
vote
0answers
42 views

Sum over multiindex

I would like to calculate a sum over some multi-indices, that follow a specific pattern. $$\sum\limits_{1\le i_1<i_2<...<i_k\le N} A(k,i_1, i_2, ..., i_k).$$ $A$ is a fix expression of the ...
0
votes
5answers
90 views

Total of summed objects of unequal lengths

I obtained {1}+{0,2}+{0,0,1}from a calculation. Now I need to sum these objects and reach 4. How can I do this? I tried ...
1
vote
1answer
58 views

Is there a way to exclude certain numbers in a sequence?

For example, the sequence of triangular numbers can be expressed as $1/2 [n (n + 1)]$ with $n=1,2,3,4,...$ but is it possible to create a summation of everything remaining $(2,4,5,7,8,9,11,12,13,14,......
0
votes
0answers
64 views

Summation together

I have the terms: ...
1
vote
1answer
49 views

Recognizing Summation Indices in Mathematica

Consider some complicated expression like the following: $$ Q[a,b]Q[a,c]M[a,c]M[a,b]$$ Where the lower case letters are matrix indices. I am looking for a way to make mathematica recognize all the ...
0
votes
1answer
53 views

How to evaluate sum only when the function is specified explicitly?

How does one instruct Mathematica to perform the following infinite sum only if the function U is specified explicitly? ...
0
votes
1answer
26 views

Minimization of a summation of two functions with respect to two constrained variables

I have a question regarding the minimization of a function, which is a summation of two separate functions, with a discrete list for one of the variables. $S[a,c]= \sqrt{\sum_{b=0,4,8,12,16}{(f[b]-g[...
1
vote
1answer
78 views

Summing over a list

I intend to sum a series over two lists which I generate myself. However, my code is not working. What is the best way to do this? Thanks. Find my code below ...
0
votes
0answers
65 views

Solving a sum involving a distribution

Can anyone help me solve this sum? ...
2
votes
0answers
96 views

Why these sums return the same result given seemingly they should be different? [closed]

This Sum[1, {k, 1, Infinity}, Regularization -> Dirichlet] gives -1/2, which is right. This ...
0
votes
0answers
42 views

how can I solve this sum?

how can I solve this sum? Sum[1/(x[p]-x[q]),{p,1,l},p\[NotEqual]q] I tried these codes but not workin' ...
0
votes
1answer
33 views

Forcing nice positions of summation Σ 's under and overscript in FractionBox

Apologies if this has been asked before. The expression ...
1
vote
1answer
49 views

Summation of terms involving contractions with 3 Levi Civita tensors

I am trying to evaluate this expression: $\epsilon^{abcdef}X^R_a X^S_b X^T_c X^U_d X^V_e X^W_f \epsilon_{RST} \epsilon_{UVW}$ where: $X = \frac{a^2 +b^2-1}{2a} \mathbb 1_6$ and I wrote this code ...
0
votes
1answer
83 views

Compute inner product of using a double sum vector [closed]

I am struggling to create a vector in Mathematica to compute an inner product. The first vector whose elements are generated over the sum over $m$ is $$a = \sum_{m=0}^n\sum_{r=0}^m C_r a_m + \sum_{m=...
0
votes
0answers
45 views

Proper Replacement Rule for Multiplying Power Series?

I am trying to evaluate the Cauchy-Riemann product of series $$\bigg(\sum_{i=0}^\infty a_ix^i\bigg)\bigg(\sum_{j=0}^\infty b_jx^i\bigg)=\sum_{i=0}^\infty \big(\sum_{j=0}^ia_ib_{i-j}\big)x^i.$$ I have ...
0
votes
1answer
97 views

NIntegrate stuck without any warning

My problem is to compute W: ...
3
votes
1answer
173 views

Sum in Mathematica gives extra “+List” [closed]

I am just doing the following sum over a list t = Table[i^2, {i, 10}] Sum[t[[i]], {i, 0, 4}] However, the output is ...
2
votes
0answers
51 views

How to evaluate $\sum_{i=1}^{n-k+1} i \binom{n-i}{k-1}$ to get $\binom{n+1}{k+1}$?

I evaluate the following summation using mma (Version: 11.2.0.0): $$\sum_{i=1}^{n-k+1} i \binom{n-i}{k-1}$$ ...
1
vote
1answer
52 views

Sum of part of a list that increases in length

I have a list of numbers whose length increases by 1 for every iteration of a loop. I need to take the sum of the last 5 elements of the list, and if the list's length is smaller than 1 I need to have ...
2
votes
1answer
55 views

Nested ordered summation

How can I implement the following sum? Given $n$ and $j<n$: $$\sum_{k_j=1}^{n-1}\sum_{k_{j-1}=1}^{k_j-1}\sum_{k_{j-2}=1}^{k_{j-1}-1}\dots\sum_{k_1=1}^{k_2-1} \phi_{(n-k_j)}[\phi_{(k_j-k_{j-1})}[\...
2
votes
1answer
51 views

Sum using variables then evaluated with values gives different result than sum with values

I'm trying to do a sum symbolically. However, Mathematica is giving me a different result if I do the sum with numbers or symbols. What's causing this error? ...
0
votes
0answers
22 views

How do I get all possible sums of all elements in two lists? [duplicate]

I want to create the sum of two lists/vectors such that every element of the first list is added to every element of the other list. I do not want to get "higher order" sums. To illustrate: ...
0
votes
0answers
50 views

Non trivial summation

I want to do the following summation over m going from $-\infty$ to $\infty$. Here $x$ is the position, $t$ is the time, $v_F$ and $v_h$ are velocities, $\beta$ is $...
10
votes
3answers
1k views

How can I compute a Kronecker sum in Mathematica?

There is Kronecker product but there is no Kronecker sum? It seems like a very important features to include. So in the absence of a Kronecker sum function, how can I construct my own Kronecker sum $...
5
votes
2answers
281 views

Expanding a sum without evaluating it [duplicate]

I am currently trying to expand a sum without evaluating it, e.g. $$\sum_{i=0}^5 i^2 = 1^2+2^2+3^2+4^2+5^2$$ So I am trying to create a function ...
8
votes
2answers
562 views

What is wrong with my use of Summation?

I want to compute $r$ according to the following code: ...
0
votes
1answer
47 views

Summations of Lists

I'm trying to find how many numbers between 1 and 1000, which are not either prime or the sum of successive primes. I've managed to create the list of all the primes between 1 and 1000: ...
0
votes
2answers
79 views

Algorithm for Swapping indices and simplifying the summand in a double sum [closed]

Say we have something like $$ \sum_{p}^N\sum_{q}^N \cos(p) \sin(q) - \cos(q)\sin(p) $$ usually, in the case like this, the indices p and q can be swapped, and the sum simplifies to 0. I have an ...
2
votes
2answers
90 views

How to make lists the same size?

I want to add 19 lists together and then average over them but they are of unequal length. How do I make then all the same length? i.e. make them all the length of the smallest one. My lists are ...
2
votes
1answer
69 views

How to plot this double sum? [duplicate]

I want to plot solution of some physics problem that I solved (for r between 1 and 2 and for f between 0 and Pi). I tried it myself but since I am beginner in using Wolfram Mathematica I have not ...
2
votes
3answers
133 views

A restricted summation over a function of integer n-tuple

I want to sum over a function of n-tuple like so: $\sum\limits_{a\leq k_1+k_2+...+k_n\leq b}f(\{k_i\}_{i=1}^{n})$ where each $k_i$ is non-negative, i.e. $k_i\geq0 \;\forall\;i $ An Example: Say, ...
3
votes
2answers
118 views

Symbolic representation of a Bézier curve

The Bézier curve is defined by: $$C(t)=\sum_{i=0}^{n} {{n}\choose{i}} t^i (1-t)^{n-i} P_i$$ where the $P_i$ are the control points. I am trying to write it down in Mathematica. What I have is: <...
4
votes
1answer
65 views

sum simplification

I have this sum Sum[-E^(-j (x kx[p] + y ky[q] + z kz[r])) j g w ky[q] Ux[p, q, r], {p, -∞, ∞}, {q, -∞, ∞}, {r, -∞, ∞}] and I would like to pull constants ...
1
vote
3answers
76 views

Improving the sum over dummy indexes

I have the following tensor ...
1
vote
3answers
186 views

Plotting Solution to Heat Equation

By hand, I've solved the heat equation and looking to 3D plot the solution. My function is $$2\sum_{n=1}^{\infty}\frac{(-1)^n}{n}\sin(nx)e^{-111n^2t}$$ The code I've been trying to use to far is <...
-1
votes
1answer
35 views

RecursionLimit error when summing over partitions

I'm computing a recursion of polynomials W[g,n] (which is polynomial in L[1],...,L[n], but keep running into the recursion depth error. I have determined which part of the recursion is causing this, ...
2
votes
2answers
81 views

Problem when defining a function as a finite sum

I am using Mathematica 8.0.1.0. I defined the following function for use in an answer on math.SE: f[j_] := Sum[1/(j-2k+1)/4^k, {k, 0, Floor[j/2]}] I then used ...
0
votes
3answers
201 views

Gravitational potential of a cube

I want to write code that calculates the gravitational potential of an arbitrarily shaped celestial body. To understand the calculation, I started with an easy shape: a rectangle (or a cube). I ...
2
votes
1answer
68 views

Abs[.] breaks my infinite sum

The following evaluates correctly to pi^2/4: Sum[n^2 (Sin[n π]/(-1 + n^2))^2, {n, 1, ∞}] The following gives a 1/0 error: ...
0
votes
1answer
67 views

Determining the distribution and other characteristics of a variable defined by a recurrence relation

I want to determine the distribution and some other characteristics of a recursive defined variable and need hereby some help/advice. I have the recurrence relation $\qquad X_t = X_{t-1} + \phi (\...
17
votes
3answers
3k views

Mathematica thinks (-1)^n is non-real

When I ask Mathematica to evaluate NSum[((-1)^n)/n, {n, 1, 100}] it returns -0.688172 + 2.11297*10^-16 i Why is this? (-1)^n is either 1 or -1. I don't know why ...