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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$\sum_{i=0}^N r^\frac{1}{a+bi}$ =?

Is there a formula for the sum of the series $\displaystyle \sum_{i=0}^N r^{1/(a+bi)}$ similar to $\displaystyle \sum_{i=0}^N r^i =\frac{1-r^N}{1-r}$ ? $a$ and $b$ are constants. Thanks for your help.
Jani
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Manipulating a Summation Series

Summation: How does$$\begin{align*} & \frac 12\sum\limits_{k=1}^n\frac 1{2k-1}+\frac 12\sum\limits_{k=1}^n\frac 1{2k+1}-\frac 12\sum\limits_{k=1}^n\frac 1k+\frac n{2n+1}\tag1\\ & =\sum\limits_{k=1}^n\frac 1{2k-1}-\frac 12\sum\limits_{k=1}^n\frac…
Crescendo
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What is the algebraic equivalent to $\sum _{n=0}^xa^{-n}$?

In this equation A is constant. I am trying to convert it into an algebraic equation so I can easily solve for "x". When I graphed it I noticed it looked like something I should be able to match to an easy function but I am unable to.
J.Doe
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Finding the infinite sum of the series

I have the series $a_n(x) = x^n \dot{} a (b^n - c^n)$ where a b and c are constants. I want to find the sum of $$\sum_{n=1}^{\infty} a_n(x)$$ for any value of x (less than one of course). I learned in algebra 2 how to find the infinite sum for just…
Ryan
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How to find limit of $\sum\limits_{k = 1}^{n - 1}(1 + \frac{k}{n})sin\frac{k\pi}{n^2}$

How to find limit of $\sum\limits_{k = 1}^{n - 1}(1 + \frac{k}{n})sin\frac{k\pi}{n^2}$ What i should to do then see sums like this?
Eugene Korotkov
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Finding the value to which a series converge.

The problem is the following: I found, in a previous exercise, that $$\sum_0^\infty{x^k}=\frac{1}{1-x}, \space for\space|x|<1$$, and in the following exercise, it asks me to apply that result to solve the following:…
Walther Wennholz Johnson
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If $q_i = q_j$ for all $i \neq j$ what's $\sum_{i=1}^n{\sum_{j=1}^{i-1}{q_i q_j}}$? (need confirmation)

I need to evaluate the following sum and wanna recheck here that I'm not mistaken. So can you please verify the corrctness or hint me to a mistake \begin{align} &\sum_{i=1}^n{\sum_{j=1}^{i-1}{q_i q_j}}\\ = &q_1q_2 + \ldots + q_1 q_n + q_2q_3 +…
clueless
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How can I write this sum compactly?

I found this sum while trying solving the Hermite differential equation by series. $$x+x*(4-x)+x*(4-x)*(8-x)+..... $$
Isai Dávila Cuba
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Simplifying the Summation of Summations: $ \sum_{n = 0}^{w}({ \sum_{k = n}^{2n} (k) })$

My question is about the simplification of the following summation: $\sum_{n = 0}^{w}({ \sum_{k = n}^{2n} (k) })$. I have used Mathematica and obtained that $ \sum_{n = 0}^{w}({ \sum_{k = n}^{2n} (k) }) = \frac{1}{2} w (w + 1) (w + 2)$. Even though…
Kiwii
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What is the difference between these two sets of symbols?

I am considering two sets of symbols. Are these two sets different or the same? Why? \begin{align}(1)\qquad&\lim_{n\to\infty}\sum_{j=1}^n\\ (2)\qquad&\sum_{j=1}^\infty\end{align}
Math12345
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When can the limit of a sum be the sum of a limit?

If I have a limit of an infinite sum, can I bring the limit inside the infinite sum? If so, why?
Math12345
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Extract a variable from the following summation

Is it possible to extract the variable a from the following summation and hence write the summation as a times 'something', or similar? $$n/a = \sum_{i=1}^n 1/(a+x_i)$$
tony1kenobi
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Can a summation of logs be simplified?

Probably a very easy question, but I can't find a simplification for the following: $$\sum_{i=1}^n\log(a_i)$$ Can this summation be simplified?
tony1kenobi
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Can I more simply express this summation?

I've been trying to make the below equation more simple such like binomial theorem: $\sum^{n}_{i=0} \binom ni a^ib^{n-i}=(a+b)^n$. The equation I want to make more simple is : $\sum^{n-1}_{i=0} \binom ni i! x^{-i}$. Does anybody have any idea to…
hoesang choi
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An infinite summation involving binomial coefficient

The question is to find out the value of $$\sum_{n=k}^{\infty} P^n \binom nk (1/2)^n$$ I tried to break down the binomial coefficient and bring it in form of some known sequence but could not get anything out of it.Please help me in this…
Navin
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