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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How to interpret a summation equation with two separated sigmas and no operator

I'm trying to write stata code to recreate a probability estimate via this published equation, but I don't understand how the two summations relate to one another since there's no operator. Obviously pretty rusty on my summation algebra, so any…
Alex T.
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Closed form of Gaussian-like summation?

I want to evaluate $$\sum^\infty_{n=1}e^{-n^2}$$ My attempt is to evaluate $$\oint_{|z|=\infty}\pi\cot(\pi z)e^{-z^2}dz$$ and prove the circular integral tends to zero. Unfortunately, this is clearly not the case. Any suggestions?
Szeto
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First derivative of a summation (looking for the steps)

What is the first derivative $\dfrac{dF}{d\zeta}$ of the following function F = $\zeta+\sum_{k=1}^{N} \dfrac{m_k}{\zeta^k}$ Thank you!
BeeTiau
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Solve for the upper limit of a summation

$a,b$ and $c$ are all natural numbers, and function $f(x)$ always returns a natural number. If$$ \sum_{n=b}^{a} f(n) = c,$$ in terms of $b,c$ and $f$, how would you solve for $a$? Do I require more information to solve for $a$? EDIT: If $x$ …
V..
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$\sum _{j,m}u_{j}c_{j,m}U_{m}$

General interpretation When given a summation as below, what is the comen interpretation when no more details are given apart from j,m being part of the positive integers. Are we given $(j,m)$, taking the sum $(1,1),(1,2),(1,n),(2,1),(n,1)....$…
ALEXANDER
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How can I compute sum of $i 4^i$?

How can I compute $$\sum_{i=0}^n i 4^i$$ this equation? What is the way?
haram
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Let $f(n)=\frac{3^{2n}}{3^{2n}+3},$ calculate $\sum_{k=1}^{2018} f \left(\frac{k}{2019}\right)$

Let $f(n)=\frac{3^{2n}}{3^{2n}+3}$. Find $$f \left(\frac{1}{2019}\right)+f\left(\frac{2}{2019}\right)+f\left(\frac{3}{2019}\right)+...+f\left(\frac{2018}{2019}\right).$$
user537970
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$\sum_{i=-1}^{99} 2^i$ Solution Assistance

So i have a general understanding of summations The problem i have is this $$\sum_{i=-1}^{99}2^i$$ I simplified it to $$\sum_{i=1}^{101} 2^{i - 2}$$ But i keep getting stuck here when trying to eliminate the sum by subbing in for i.
Yam
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Solution of sum

What is an easy way to find the solution of this sum? $$\displaystyle\sum_{i=1}^{\infty} i3\Bigg(\frac{1}{3}\Bigg)^{i+1}$$ wolframalpha solution: $\frac{3}{4}$
Muradin Bronzebeard
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What's the summation of a square root of a quadratic function?

Is it possible to do such a sum? $$\sum_{i=1}^n \sqrt (i^2+\frac{8i}{n}+\frac{16+n^2}{n^2})$$ I want to reach to a function with only the n as variable. I believe that it is possible somehow by squaring the summation and squaring the other side of…
Mac Spour
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Computing closed form summations

Problem: Compute the close form for $\sum_{i=1}^n \sum_{j=1}^n \sum_{k=1}^n (3i-1)$ as a polynomial in n. The closed form solution should not have a summation in it. I am not used to working with multiple summations so I'm not sure if I erred in…
Jessica Tiberio
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how to rewrite this equation to solve for P?

I have following equation, How could I rewrite this equation that I could solve it for P? Ni is number of counts in i, N is the total number of counts, S(n) is a known function, the C part is binomial coefficient and P is actually the probability.
Nikki
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Geometric Summations that reference two variables

Hello math stackexchange! I'm new here so please correct any formatting mistakes I make / I'm happy to provide more info if needed. I have a summation of the form $\sum_{i=1}^{n} \sum_{j=1}^{i} (i+j)$, and I'm not too sure how to go about solving…
BitShuffler
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Show that this equation is equal to $\sum_{k=2}^{2n+1}\frac{2}{k^2-1}$

Show that this... $\sum_{k=2}^{2n+1}\frac{2}{k^2-1}= \frac{3}{2}-\frac{1}{2n+1}-\frac{1}{2n+2}$ I have already arrived at... 1+ $\frac{1}{2}$ + ($\frac{1}{2n-1}$ - $\frac{1}{2n+1}$) + ($\frac{1}{2n}$ - $\frac{1}{2n+2}$) But I am unaware as to how to…
L. Li
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Why is $\sum_{j=i+1}^{n-1}1 = -i+n-1$?

Why is $\sum_{j=i+1}^{n-1}1 = -i+n-1$? I am having trouble understanding this result, we are summing up $1$ from $i+1$ to $n-1$ wouldn't that just be $1$?
bigfocalchord
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