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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Summation Rules/Dividing Sums

Is there a way to simplify the following expression? $${\sum_{i=1}^n (1-g(x))^{i-1}} \over {\sum_{i=1}^n (1-g(x))^i} $$ With $0
PAS
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Solution to elementary summation

I am trying to evaluate the following expression: $$(1)+(1+2)+(1+2+3)+(1+2+3+4)+...+(1+2+3+4+...+(N-1)+N) \\ =\sum\limits_{n=1}^N\frac{n(n+1)}{2}$$ Hopefully someone can give me a closed-form solution, otherwise just a general idea of whether this…
高田航
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Question on powers in a sum/series of real numbers

Usually when we have a sum that depends on the power of a real number, we write the null power as $1$. For example, the series $$e^x = \sum_{k=0}^{\inf} \frac {x^k} {k!}$$ However, this doesn't work for zero, since $e^0 = 1$ but the series should be…
Francisco José Letterio
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Clarity on the following summation rule

Consider the following summation rule: $$\sum_{k=1}^n c=nc$$ given that this is true, it implies that $$\sum_{k=0}^{n}c=(n+1)c$$ and the question is, does this imply that the general case is $$\sum_{k=r}^nc=(n-r+1)c$$ I'm asking because I had to…
joshuaheckroodt
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how to solve the summation

This question might have been asked before but I have not been able to find it. How can I find: $$\sum_{i=0}^n 2^{x-i}$$ Help?
Lucas
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Unclear Index of Sum

I'm facing this sum of products $\sum_{j, k=1; j\neq k}^{3}\theta_j \theta_k$. Now, does this mean ${1\times2 + 1\times3 + 2\times1 + 2\times3 + 3\times1 + 3\times2}$ or just ${1\times2 + 1\times3 + 2\times3}$? Thanks.
jay.sf
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Summation notation of X^2

Is this correct? If so a link to more information/proof would be appreciated. Thanks! $$\sum_{k=1}^x(k + k - 1) = x^2$$ WolframAlpha
ID10T_ERROR
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How do I approach this question

From my search the summation cyc denote summations over permutations. But now there's a set involved, and I feel quite lost on how to put the meaning of it all together and how to proceed.
Long Vuong
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Evaluating the sum $\sum_{n = 0}^{n = \infty} a^n cos(n\theta)$

I have seen a similar question to this asked previously: Proving $\sum\limits_{k=0}^{n}\cos(kx)=\frac{1}{2}+\frac{\sin(\frac{2n+1}{2}x)}{2\sin(x/2)}$ but I was playing around with the sum $\sum_{n = 0}^{n = \infty} x^n = \frac{1}{1 - x}$ (for $|x| <…
user8742633
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Sigma Series Formula

I have two examples of sigma summation, where $n$ & $j$ are positive integers and $c$ & $x$ are any real or complex numbers. The first makes complete sense to me, however; the second partially doesn't. So, for i) I understand that I am just adding…
Lo-urc
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Variation of the sum of 1 / (n +k) with k =1, to n

Could you help me find the variation of the sum sequence $$S(n)=\sum^n_{k=1}(n+k).$$ I tried to do $S(n+1) - S(n)$ but I can't simplify. Any ideas?
lolodino77
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Summation Notation?

A question I've come across says that $\sum_{n=1}^{10} a = 50$. Okay, so far so good. Then it asks me to find $\sum_{n=1}^{10} (4a + 3)$. I looked at the answer and found it was 230, but I just can't figure out why. My best guess would be 203, but…
Caleb Bertrand
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What is the sum of the series where $a_n = an^{log_b(n)}$

I'm struggling with a growth model and finding a formula to describe the growth. I've managed to figure out $a_n = an^{log_b(n)}$ but now need to find a formula for the sum of the series $S_n = f(n)$ Thanks in advance,
Ishai Smadja
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finding the sum of $f(k)=\sum_{n=1}^k a*n^{log(n)}$

I am trying to find the sum of: $$f(k)=\sum_{n=1}^k a*n^{log(n)}$$ Would appreciate help, Thanks!
Ishai Smadja
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4 answers

$\sum_{i=0}^n 2^{-i}$

This question might have been asked before but I have not been able to find it. How can I find: $$\sum_{i=0}^n 2^{-i}$$ Help?
Lucas
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