Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [summation]

Questions about evaluating summations, especially finite summations. For infinite series, please consider the (sequences-and-series) tag instead.

The notation $\sum\limits_{i=1}^na_i$ means $a_1+\ldots +a_n$.

Use for sums of infinite series and questions of convergence; use for questions about finite sums and simplification of expressions involving sums.

17770 questions
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Writing a formula in terms of $a_m$

I have derived a formula, which is: $$a_m=\sum^m_{i=0}\binom{m-i}{n-i}b_ik^{m-i}, m\geq n$$ The main problem is to write the formula in terms of $a_m$, or means that we can find $a_m$ using $b_i$, can anyone help?
xxxx036
  • 773
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Finding $2 \pi \sum_{i=0}^N \left(1 - \frac{a}{a + b - i c}\right)^{\frac{3}{2}}$

Is it possible to solve the following series? $$2 \pi \sum_{i=0}^N \left(1 - \frac{a}{a + b - i c}\right)^{\frac{3}{2}}$$ where $a,b,c$ are parameters. Since $a \gg b,c,N$, solving the Taylor expansion might also do the trick: $$3 \pi \sum_{i=0}^N…
Babababa31
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Better way to write the sum of multiple terms with cross-correlation

how can I write this expression using summation? $y^2=x_1^2 + x_2^2 + x_3^2 + x_4^2 + 2x_1x_2 + 2x_1x_3 + 2x_1x_4 + 2x_2x_3 + 2x_2x_4 + 2x_3x_4$
Dealer
  • 11
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What Identity is used in this proof

I'm currently working through a proof and I'm stuck at figuring out how $\sum_{i=1}^n ((\sum_{j=1}^k C_{ij})^2)$ becomes $\sum_{i=1}^n \sum_{j=1}^k C_{ij}^2 + 2\sum_{i=1}^n \sum_{j=1}^k \sum_{h=1, h \neq j}^k C_{ij}C_{ih}$ I've tried working through…
Cody R.
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Reducing sum of squared differences to closed form expression

I have the following expression: $$\sum_{i=0}^{n-1}[\rho^i-\frac{1}{n}(\frac{\rho^{i+1}-1}{\rho-1})]^2 $$ I would like to reduce this to a closed form expression. What I have tried so far: Remove the square by multiplying out. This give an inner…
RVA92
  • 115
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When can I say $\int\limits_{-T}^{T} \sum_n\sum_m f(m.n.t)dt=\sum_n\sum_m \int ^T_{-T}f(m,n,t)dt$?

When can I say $\int\limits_{-T}^{T} \sum_n\sum_m f(m.n.t)dt=\sum_n\sum_m \int ^T_{-T}f(m,n,t)dt$? All I know is that for each $t\in[-T,T]$, $\sum_n\sum_m f(m,n,t)$ is absolutely convergent, which I think is farily strong condition. But now I can't…
jk001
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Stuck on Algebra for Summation Problem

I want to find what the exact value of this sum is. What I was given is: $$\sum_{i=1}^n \frac{1}{\sqrt{2i-1} + \sqrt{2i+1}}$$ The only thing I can think of is turning the denominator into the form: $$\sum_{i=1}^n \frac{1}{(2i-1)^{\frac{1}{2}}…
DippyDog
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How to find fundamental period of summation function?

I cant seem to understand how to find the fundamental period from this exponential function. $$\large x(t)=\sum _{k=2}^{k=14} e^{ j k\frac{2\pi}{7} t}$$ I'd really appreciate any help, I cant find much anywhere
anon
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Convergence of a Special Series as N is large

I'm trying to find a general formula for the series and x is a constant: $$\sum\limits_{i=1}^N \frac{i}{(1+r)^i}$$ I have deduced the general formula for the sum. $$\frac{(1+r)^{N+1}-(1+r)-rN}{r^2(1+r)^N}$$ Will this sum converge to some value when…
Cindy Philip
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Calculate the following series --- need to understand why I have it incorrect

Okay I know I have the answer incorrect but not sure why... Calculate the following series: $$\sum_{j=0}^n 2^j \text{ for } n = 1,2,3,4$$ so I think it would be $2^1 = 2$ but the answer is $3$ and the rest are $7,9,32$... I do not understand how…
Susan.Cook5896
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How to evaluate the sum $\sum_{j=i+1}^n (j-i)$?

How would I go about solving this summation? $$\sum_{j=i+1}^n (j-i)$$ So far I have: Using variable substitution let ${k = j - i}$ $$ \sum_{j=i+1}^n (j-i) = \sum_{k=1}^{n-i} k$$ $$S = 1 + 2 + 3 + ... + (n - i)-2 + (n - i) - 1 + (n - i) $$ $$S =…
Zeus Krakus
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Double summation: how to solve?

I have this summation that I need to solve: $$\sum_{i=2}^{n}\sum_{j=i}^{n} 3i$$ Can someone please help? I have no idea how to start this
user850676
  • 35
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Manipulating a symmetric sum indices

$$ \sum_{}^{} \binom{2n+1}{i}( 6 \sqrt{6})^i 14^{2n+1-i}$$ Over the sequence, $$ i= \{1,3,5,..,2n+1 \}$$ Suppose I do the substitution, $ 2n+1 - i = j$, $$ \sum_{j}^{} \binom{2n+1}{j} ( 6 \sqrt{6})^{2n+1 -j} 14^{j}$$ Note that the value of $j$ we…
tryst with freedom
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Time complexity (easy)

I know that this platform is probably not the best place for this question, on stack overflow I didn't receive any answers. Consider the following code snippet: for (int i = n; i >= 1; i = i / 2) { for (int j = 1; j <= i; j = 2 * j) { …
Hilberto1
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Why does this formula have the summation sign?

I'm doing a programming tutorial and an algorithm to sum each number up to N can also be done by the below formula. E.g. if n = 10, 1+2..+10 = 55. Forgive me for the stupid question :) but why does the formula use the sigma notation? Could we not…
0xgareth
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