Questions using the Sum command, especially for series and other algebraic objects, and related functions such as SumConvergence
0
votes
1answer
33 views
Derivative of sum of elements of array [on hold]
I try to get derivative of sum of an array with respect to an element of the array.
$$s = \sum_{i = 1}^{3}A_{i, 1}$$
Evaluate $\frac{\partial s}{\partial A_{1,1}}$
Below is the code.
...
0
votes
2answers
39 views
Create and manipulate list with variable length?
Is there a way to create and manipulate a function of a sum of arbitrary length? Specifically, I'd like to create a function like the following:
...
0
votes
0answers
42 views
NSum: Summand (or its derivative) is not numerical at point
I am experiencing a problem in evaluating the maximum of a function that is defined as a sum
...
11
votes
4answers
236 views
Finite sum not evaluating
Mathematica refuses to evaluate this summation.
Sum[2^(k + 1)^3 - 2^(k - 1)^3, {k, 0, n}]
It just returns the form unevaluated.
$\sum _{k=0}^n \left(2^{(k+1)^...
1
vote
3answers
59 views
Sum of all the n-th numerical evaluation of an integral and its cumulative sum of the square of the n-th value
I wish to compute the expansion coefficient of a wavefunction(i.e. in quantum mechanics) which in itself is an integral, given by
$$b_{n00} = \int^{\infty}_{u = 0} \frac{1}{(n)^{3/2}} L^{1}_{n-1}\left(...
0
votes
1answer
55 views
Sum was simplified and I don't know how it was done
I want to compute the sum
$\qquad \sum_{i=1}^{n+r}(i+1)n^{i-1}(n+1)^{n+r-i}$
However, when I input the expression
...
8
votes
2answers
2k views
Wolfram says sum diverges, but Mathematica gives a numerical value for infinite sum [closed]
Take this sum for example:
$$\sum_{n=2}^\infty\frac1{\log(n!)}$$
Wolfram says that this does not converge by the comparison test. However, when I use Mathematica's ...
1
vote
4answers
96 views
Summation exercise — how can I translate the problem statement into the Wolfram Language? [closed]
I'm new to both Mathematica and this forum, so this will be my first post here. I just got into Mathematica today, and I've been doing some exercises. Up to now things have been going well, but I've ...
11
votes
0answers
80 views
What does that output of Sum mean?
I made the computation
ClearAll["Global`*"];
r = Sum[1/2^(k*n/(k + n)), {k, 1, 2*n}, Assumptions -> n ∈ Integers && n > 0]
and got
...
1
vote
2answers
63 views
Evaluating a formula that uses summations and products of vectors
Could someone tell me how to find beta1?
I have the following data:
I don't know how to write beta1, and I don't find ...
0
votes
1answer
33 views
summation syntax for defining conditions and solving
I am trying to generate datasets for which specific conditions related to the grand mean, group means, and differences among these values hold. I had tried in R, but was hoping that using Mathematica ...
-1
votes
0answers
57 views
Why is it possible to have results greater than 1 and less than 1 in $ \sum_{k=1}^{100} 0.01 $, $ \sum_{k=1}^{10000} 0.0001 $ …? [duplicate]
Mathematica gives the following results:
$ \sum_{k=1}^{100} 0.01=1.0000000000000007$
$ \sum_{k=1}^{10000} 0.0001=0.9999999999999062$
$ \sum_{k=1}^{100000} 0.00001=0.9999999999980838$
$ \sum_{k=1}^{...
5
votes
2answers
107 views
Why is $\sum\limits_{k=1}^{100} 0.01 $ different than $\sum\limits_{k=1}^{100} \frac{1}{100}$?
Why does evalutating $\sum\limits_{k=1}^{100} 0.01$ not result in 1?
What I get is 1.0000000000000007.
I know that the number 0.01 in binary results in an infinite sequence of zeros and ones, which ...
3
votes
3answers
313 views
Speeding up the calculation of a binomial sum
Is it possible to speed up this calculation?
A[j_, p_, n_] := Sum[Binomial[n, k] p^k (1 - p)^(n - k), {k, 0, j}]
Plot[{A[j, 0.5, 12000]}, {j, 0, 12000}]
Thanks!
1
vote
1answer
52 views
Simplifying a Sum of Fractions by Removing Fractions in Denominators
I have a sum of fractions of the form $x1 - \frac{(x2 + x3)}{(x4 + x5)} - \frac{(x6 + \frac{x7}{x13})}{(x8 - x9 - \frac{x10}{(x11 + x12)})}.$
How might I simplify it to remove fractions from the ...
-1
votes
1answer
38 views
Why i get “Infinite expression 1/0.^5 encountered” in summation?
this is my code
the file
https://drive.google.com/open?id=1foOFbyAnn4buPgHq_LvF5eGjZYm4SEM-
...
1
vote
1answer
37 views
Create list of values with arbitrary index and the use it in a function
I have the following generating functions:
$l_{2i-1}=l_{1}-(i-2)(w+s)$ with $i\geq 2$ and
$l_{2i}=l_{2}-(i-1)(w+s)$ with $i\geq 2$, so the first one is for odd index and the second for even index. ...
3
votes
0answers
74 views
Summation of the multipole expansions [closed]
Let $ \vec\Omega, \vec\Omega' $ be two unit vectors in $ \mathbb R^3 $ such that $ \vec\Omega\cdot\vec\Omega' = t $ and let $ r > 0 $. The multipole expansion for the exponential reads:
$$
\...
3
votes
0answers
147 views
On Ж, and the fine-structure constant
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 ...
2
votes
1answer
79 views
Computing numerically infinite sum of some double series
Let's consider the series:
$$
F(t) = \sum\limits_{n=0}^{\infty}\sum\limits_{k=0}^{\infty}
\frac{(-b)^k(-a)^n\binom{n+k}{k} t^{2n+k(2-\alpha)}}{\Gamma(2n+k(2-\alpha)+2)}
$$
where $a,b$ are ...
-1
votes
2answers
56 views
Please help me get the ratio of x to y [closed]
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
172 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 ...
3
votes
1answer
36 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
40 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 ...
5
votes
2answers
111 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
38 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
57 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
vote
0answers
53 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
93 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
63 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
67 views
1
vote
1answer
55 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
57 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
27 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
82 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
45 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
35 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
50 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
85 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
$$a = \sum_{m=0}^n\sum_{r=0}^m C_r a_m + \sum_{m=...
0
votes
0answers
48 views
Proper Replacement Rule for Multiplying Power Series?
I am trying to evaluate the Cauchy-Riemann product of series $$\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.$$
I have ...
0
votes
1answer
101 views
3
votes
1answer
174 views
Sum in Mathematica gives extra “+List” [closed]
I am just doing the following sum over a list
t = Table[i^2, {i, 10}]
Sum[t[[i]], {i, 0, 4}]
However, the output is
...
2
votes
0answers
52 views
How to evaluate $\sum_{i=1}^{n-k+1} i \binom{n-i}{k-1}$ to get $\binom{n+1}{k+1}$?
I evaluate the following summation using mma (Version: 11.2.0.0):
$$\sum_{i=1}^{n-k+1} i \binom{n-i}{k-1}$$
...
1
vote
1answer
57 views
Sum of part of a list that increases in length
I have a list of numbers whose length increases by 1 for every iteration of a loop. I need to take the sum of the last 5 elements of the list, and if the list's length is smaller than 1 I need to have ...
2
votes
1answer
58 views
Nested ordered summation
How can I implement the following sum?
Given $n$ and $j<n$:
$$\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
25 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 $...
