All Questions
21
questions
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Getting the formular of a summation [duplicate]
im kind of stuck at my math homework from my calculus class. To progress further i need to be able to write a Summation into a forumular(?), as seen in the picture. Is there any proven method to do ...
- 1
1
vote
1
answer
109
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How to factorize and solve equations with $\Sigma$ notation?
I have a few doubts about the properties of sigma notation, $\Sigma$ . My questions rely on factorization and solving equations with $\Sigma$.On account of the fact that my questions are correlated, I ...
user1056027
0
votes
2
answers
293
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How do I solve the double summation $ \sum_{n=1}^{\infty} \sum_{m=1}^{\infty} \frac{m^2 - n^2}{(m^2 + n^2)^2}$?
Basically I'm stuck with this double summation. I want some help evaluating this summation.
$$ \sum_{n=1}^{\infty} \sum_{m=1}^{\infty} \frac{m^2 - n^2}{(m^2 + n^2)^2} $$
Am I allowed to change the ...
- 37
0
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0
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96
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Alternative method to showing that $\sum_{r=-\infty}^{\infty}\frac{1}{64r^4+1}=\frac{\pi}{4}\frac{1+\sinh(\pi/2)}{\cosh(\pi/2)}$
In my answer to this question I proved the fact that $$\sum_{r=-\infty}^{\infty}\frac{1}{64r^4+1}=\frac{\pi}{4}\frac{1+\mathrm{sinh}(\pi/2)}{\mathrm{cosh}(\pi/2)}$$
using quite a non-advanced method*; ...
- 6,560
2
votes
5
answers
223
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How do I evaluate $\sum_{n=1}^{\infty}\frac{n}{2n-1} - \frac{n+2}{2n+3}$? [closed]
$$\sum_{n=1}^{\infty}\frac{n}{2n-1} - \frac{n+2}{2n+3}$$
I've tried combining the sum, telescoping series and even trying to make an Nth partial sum but nothing seems to budge. I'm not sure where to ...
- 137
0
votes
1
answer
39
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Why this iteration summation is wrong when I calculate it?
$V_n = 3^{n}$
I need to calculate its summation where
$S = (V_0)^{2} + (V_1)^{2} + ... + (V_{n-1})^2 $
Obviously, you can just put a new iteration $(W_n)$ where $W_n = (V_n)^{2}$ You find it $W_n = 9^{...
- 433
2
votes
2
answers
76
views
Evaluating a sum without using a program
$$ \sum_{k=1}^{\infty} \frac{e^k}{k^k} $$
The solution is about $\approx {5.5804}$
But I don't know how to calculate this sum, I tried using the squeeze theorem but I couldn't find $2$ series that ...
user757932
1
vote
3
answers
1k
views
it's possible to invert summation/ series limits?
If the summation just sum every term i was thinking that for instance 1+2+3+4 = 4+3+2+1
so why this $$\sum\limits_{i=1}^{n} (3i)\ = \sum\limits_{i=n}^{1} (3i) $$ is not true ?
And how i can ...
- 241
1
vote
1
answer
42
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Calculator disagrees with my summation calculation?
I’m given a very elementary problem. Solve the following summation for $n=100$:
$$\Sigma_{k=1}^n (5-4k)$$
Which I solve as follows:
$$\Sigma_{k=1}^n 5 - 4\Sigma_{k=1}^n k$$
Which simplifies to:
$$5n - ...
- 331
4
votes
0
answers
297
views
Finding a general way to sum $ \sum_{i=1}^{i=n} i^k$ for a given 'k' using elementary highschool calculus [duplicate]
Today morning I had thought of a wonderful way to calculate the general sum of $$ \sum_{i=0}^{i=n} i^n$$
Using just things taught in elementary high school calculus. So, my method is as follows,
First ...
-2
votes
3
answers
65
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Summation problem: find k if $\sum_{k=5}^{29} kn-6=1125$ [closed]
How do I find k if $\sum_{k=5}^{29} kn-6=1125$ ? I tried to solve it but couldn’t understand it. Any hints would be appreciated!
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0
votes
1
answer
87
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General formula for the sum of x raised to general degree: $(1^z + 2^z + \cdots+ x^z)$
As I was reading a book on the financial market micro-structure, I came across a simplification that I have not been able to prove.
The book states that $\sum_{\ell=1}^{Q}2G_0(\frac{1+\gamma}{\ell})\...
- 175
0
votes
0
answers
52
views
Finding total of matrix, fraction with two variables
I'm trying to solve summation over a matrix that has been populated with an equation using two variables.
Trying to derive the a matrix populated with the equation:
$$f(x,y) = \frac{a}{x^2 + y - b}$...
- 53
0
votes
2
answers
47
views
How do I notate this?
Let’s say that I have a whole pie, and I take $75\%$ (or 3/4ths) of that pie. Then, I take $75\%$ of the remaining quarter of the pie and add it to the original $75\%$, I would have $93.7\%$ of the ...
- 95
2
votes
1
answer
90
views
Sum to $n$ terms the series $\frac{1}{3\cdot9\cdot11}+\frac{1}{5\cdot11\cdot13}+\frac{1}{7\cdot13\cdot15}+\cdots$.
Q:Sum to n terms the series :
$$\frac{1}{3\cdot9\cdot11}+\frac{1}{5\cdot11\cdot13}+\frac{1}{7\cdot13\cdot15}+\cdots$$
This was asked under the heading using method of difference and ans given was
$...
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