**517 summation questions.**

I'm trying to reproduce the results from a certain infamous paper that has been moving around the web for the last few days. The details are irrelevant.
This paper claims to have a closed-form ...

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

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!

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 ...

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

I have the expressionSum[(2 j \[Pi] Sin[(2 j \[Pi] x)/(r + 1)])/(r + 1)^2, {j, 0, r}] == 0I want to find the roots in terms of ...

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 ...

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 ...

I am trying to find the sum $$\sum _{k=1}^n
\frac{k+1}{(k-1)!+k!+(k+1)!
}.$$
I triedSimplify[Sum[(k + 1)/(( k - 1)! + k! + (k + 1)!), {k, 1, n}]]and got
...

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 ...

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 ...

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,......

I have the following expressionF[p1, p2] a[p1] ** b[p2] - F[p1, p2] a[p2] ** b[p1]where ** is the non-commutative ...

I wish to compute compute terms like Sum[f[t[j[1]],t[j[2]],...],{j[1],m},{j[2],n},...] for arbitrary positive integer n and any ...

How does one instruct Mathematica to perform the following infinite sum only if the function U is specified explicitly?
...

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 ...

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[...

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
...

Can anyone help me solve this sum?
...

ThisSum[1, {k, 1, Infinity}, Regularization -> Dirichlet]gives -1/2, which is right.
This
...

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'
...

Apologies if this has been asked before.
The expression
...

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 ...

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=...

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

Is it possible to evaluate this double summation which includes an integral with Mathematica for some given $r$?
$$\sum_{m=-\infty, m\neq 0}^\infty\sum_{n=-\infty, n\neq 0}^\infty m \int_0^{2 \pi} \...

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

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 ...

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})}[\...

There is a formula for the hypergeometric ($_2F_1$) that expresses it as a sum of Pochhammer symbols, times something that reads
$$_2F_1(a,b,c;x) = \sum_{i=0}^{\infty} \frac{(a)_i (b)_i}{(c)_i} \frac{...

I would like to evaluate this summation:
\begin{align}
\sum_{j=1}^{NM}\left[(u_{j_x} + u_{j_y})^2 - 2(1-\rho) u_{j_x} u_{j_y}\right],
\end{align}
where $NM$ is some number greater than or equal to $...

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?
...

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:
...

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 $...

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 $...

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
...

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:
...

I would like to write a code to evaluate the following (up to $N=20$)
$\sum_{s_1,...,s_N=\pm 1;s_1 \cdot \cdot \cdot s_N=1}\sum_{\sigma\in S_N}\prod_{i=1}^N x_{\sigma(i)}^{s_i \lambda_i}$
There are ...

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 (\...

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 ...

Bug introduced in 8.0 or earlier and fixed in 9.0
I have:
...

I am required to computed following Expectations :
$E[\displaystyle\sum\limits_{i=1}^N \frac{X_{i}}{N}] = \bar{x}_{0}$ & $E[\displaystyle(\sum\limits_{i=1}^N \frac{X_{i}}{N})^2] = \frac{(N\bar{x}...

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 ...

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 ...

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<...

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