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 of cosine value from 0degrees to 89degrees

I am unable to solve the summation of cosine value from 0 to 89 degrees. Please help me. Thank you.
Aayush Meshram
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Rewriting the Index of Summation

Suppose I have a summation of the form $\sum\limits_{n=0}^\infty n(n-1) c_n x^{n-2}$. As is done in my textbook, we can replace $n$ with $n + 2$ and begin the summation at $n = 2$ instead of $n = 0$, giving us $\sum\limits_{n=2}^{\infty} (n+2)(n+1)…
user465188
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Simplifying $\sum_{ m = - \infty}^{\infty} e^{-am^2/2 + bm}$

Is there any way to simplify an expression like this $\sum_{ m = - \infty}^{\infty} e^{-am^2/2 + bm}$? I know there exist an identity for a similar expression, just integrating, does the same identity still hold for the summation case? If so, how…
user110320
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Summation Simplication

$$\sum_{y\,:\,y=x} P(x,y) = P(x,x)$$ How did the summation get removed? I expected it to simplify into $$\sum_{y\,:\,y=x} P(x,x)$$ or $$\sum_{all \, x} P(x,x)$$
A_for_ Abacus
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Stuck with a sum problem (change of lower bound)

This is from a solution to a problem (3b here). I can't understand why the highlighted parts are equal. I've figured out that $\sum_{i=a}^b i$ is the same as $\sum_{i=1}^{b-a+1} (i+b-a)$. The bounds on the second sum agree with that. $b$ and $1$…
Tim
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How to find partial and infinite sum of $\sum\limits_{n=0}^{m}\frac{1}{(na+b)^k}$ (if $a,b$ - constants)?

How can I find partial sum of $$\sum\limits_{n=0}^{m}\frac{1}{na+b}$$ and infinite sum of $$\sum\limits_{n=0}^{\infty}\frac{1}{(na+b)^k}$$ if $k>1$ and $a,b$ - constants? I sure it simple, but really have no ideas.
user514787
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For given $k,N\in\mathbb{N}$, how to compute $\frac{\sum^N_{i=0}i^{k+1}}{\sum^N_{i=0}i^k}$?

Is it any easier than computing $\sum^N_{i=0}i^k$? I've came to such a sum while trying to solve a task from a basic course on probability... If $\frac{\sum^N_{i=0}i^{k+1}}{\sum^N_{i=0}i^k}$ can't be easily solved, then I think I'll share this task…
gaazkam
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Are there a formula for generalize nested summation?

I have played a game that have a mechanic of summation and want to write algorithm to calculate it It is a game that let you grow an insect nest. It has Ant that give you 1 food per sec. Queen give you 1 Ant per sec. Nest give you 1 Queen per…
Thaina
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Explain the following step

In an exercise the following (simplified) step was made, now I can't recall how I came to this, please explain the following step: $$... = \sum\limits_{m=0}^\infty \frac{1}{1000^m} = \frac{1}{1-\frac{1}{1000}} =... $$
Michelle_B
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sum of the sum of elementst of all subsets

Suppose you have the set $\{1,...,n\}$. What is the sum of the sum of elements of all subsets of it? I have the following reasoning: each number $1 \leq i \leq n$ appears in $\sum_{k=1}^n {n \choose {k-1}} = 2^n - 1$ subsets, and therefore we can…
TheNotMe
  • 4,841
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How do I express $\displaystyle\sum_{r+s+t=n}a_{r,s,t}$ explicitly as nested sums, where $r,s,t,n$ are positive integers?

How do I express $\displaystyle\sum_{r+s+t=n}a_{r,s,t}$ explicitly as nested sums, where $r,s,t,n$ are positive integers? That is to say, how can I express it in the following…
pshmath0
  • 10,565
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How to find answer of $\sum_{i=1}^{n}\, i^i$ and solve its equation?

I like to find a formula for the $\sum_{i=1}^n\,i^i$. It is possible to write a formula for the summation of the form $\sum_{i=1}^n\, i^a$. For example, here explain its methods completely. But what kind of method should we use when the power in the…
Doralisa
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Multi variable summation/union

I've seen a process like this in a proof: $$\sum_{k,l}|I_{k,l}|=\sum_k\sum_l|I_{k,l}|$$ and it says we can't do this if the summands are not positive numbers. I thought the left side is an abbreviation of the right side, but something's more in this…
user159234
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Is it possible to analytically solve k * ∑(1/n) = 150, n = 1 to 2k for k?

Is it possible to analytically solve the following sum for k: k * ∑(1/n), n = 1 to 2k? View the linked image to see the sum in question written in conventional notation:
K. Claesson
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Answer to the summation

I have this summation Check the image How did I get the RHS of answer?
joma dones
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