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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Inverse formula with summation

I've been struggling with what is probably some basic mathematics. I've got a summation formula which I use to calculate the 'experience' required to reach a particular 'level'. The…
Celant
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Use ratio test to find value of $\sum_{k=1}^\infty\frac{(\frac{1}{10})^{k+1}}{k(k+1)}$

I know the series $$\sum_{k=1}^\infty \frac{(\frac{1}{10})^{k+1}}{k(k+1)}$$ is equal to $$\frac{1}{10}-\frac{9}{10}\ln \Big(\frac{10}{9}\Big)$$ but how would I use the ratio test to show this is true? I also know that:…
undergrad2020
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Finding the value of $x$ within summation

I have two equations that I have to find the value of two variables within them. It also uses summation in both equation. My purpose is finding the value of $x$ and $y$. Can you help me with how to modify the equation to be like $(x = \ldots, y =…
yourmams
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summation subsets formula

I would like to know the explanation of this formula please, does it depend on Binomial distribution ? $\sum_{A\subseteq S} P ^ {|A|} (1-P)^{|S|-|A|} =1.$
Amani
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How was this summation simplified to 1/i?

How is the summation below simplified? $$\sum_{j=i+1}^{2i} \frac1{i^2} = \frac{i}{i^2} = \frac1{i}$$ Thanks!
Raoul Duke
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Double Summation Indices Switching

How can you "rigorously" prove the following mathematical fact? $$ \sum_{k=0}^m \sum_{j=0}^k a_{kj} = \sum_{j=0}^m \sum_{k=j}^m a_{kj} $$ Visually, it is clear they are equivalent (https://math.stackexchange.com/a/1395905/635480)
cosmic_inquiry
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What is the value of a summation with a larger index than it's stopping value n.

$\Sigma_{i_=n+1}^n$ I think the result will be 0 right ? My reasoning being since this would be a summation of an empty sequence.
KetDog
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How do you eliminate this constant from this summation?

I was trying to help some friends with their math homework, and I am completely stumped. Now I am curious myself on how to solve it: Determine the following sum, in terms of n: Summation from i = 0 to n, of (-1)^k * (n choose k) * 10^k These are all…
JBraha
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Estimation of summation

A question told me to estimate the summation of $$\sqrt i$$ from 0 to 10000000 using integrals $$\sum_{i=0}^{10000000}\sqrt{i}=?$$ Is it okay to estimate by integrating it from 1 to 10000000, or am I supposed to use other methods like Riemann's Sum…
Jisbon
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what is result the double sum(sigma) with assume n=3?

I'm gonna calculate the double sum on this screenshot with n=3 $$ E[X] = E \left[ \sum_{i=1}^{n-1} \sum_{j=i+1}^n X_{ij} \right] $$ what is the result I get it?! and how to calculate it? thanks
Michael
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$\sum_{i=1}^{n} (3i + 2n)$

I want to verify what would be the simplified solved version of this summation. $$\sum_{i=1}^{n} (3i + 2n)$$ Would it be this? $$ \frac32n^2 + \frac32n + 2n^2 $$
user1766555
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Can not solve Summation equation

enter image description here $$\sigma_3 = \sum_{k=0}^7 (k+2)^3 $$ in the image I have attached you can see an equation which I can not solve. However one student at my university who has solved the equation has added an 8 (+8) to the equation in…
Math Noob
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How to simplify $\sum_{k=0}^\infty \frac{(-1)^ka^{2k+1}}{(2k-1)(2k+1)!}$?

I think that this sum can be simplified so that there's no factorial in the denominator and no exponential function in the numerator. But how can I do this? $a$ - is a constant. Could anybody show me step by step solution? $$\sum_{k=0}^\infty …
Vitalii Paprotskyi
  • 217
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What is the fastest method to solve this 5-digit summation problem?

Consider the following 3 totals: 65,232 73,002 56,273 For each total listed above, identify the three numbers from the following list which, when summed up, equal each total above.…
Pete Mahon
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What is the summation of some pseudo factorial?

Given $n$ is a positive integer where $n>2$, what is the summation of the following? $$S_n=1+n+n(n-1)+n(n-1)(n-2)+\cdot\cdot\cdot+n!$$
Wz S
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