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
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
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.$$
I have ...
0
votes
1answer
97 views
3
votes
1answer
173 views
Sum in Mathematica gives extra “+List” [closed]
I am just doing the following sum over a list
t = Table[i^2, {i, 10}]
Sum[t[[i]], {i, 0, 4}]
However, the output is
...
2
votes
0answers
51 views
How to evaluate $\sum_{i=1}^{n-k+1} i \binom{n-i}{k-1}$ to get $\binom{n+1}{k+1}$?
I evaluate the following summation using mma (Version: 11.2.0.0):
$$\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
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
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 ...
