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 and Time Complexity

So I'm studying for my data structures midterm that's this monday, and my professor gave out a sample midterm with the answers, but I'm having a hard time understanding one of the questions. Here's a screen cap: Could someone give me a walk through…
Connor Black
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How many ways to evaluate $1 + e^{-x} + e^{-2x} + e^{-3x} + \ldots$ to $(e^x - 1)\cdot(e^{-x} + 2e^{-2x} +3e^{-3x} + \ldots)$

How many ways to evaluate $1 + e^{-x} + e^{-2x} + e^{-3x} + \ldots$ to $(e^x - 1)\cdot(e^{-x} + 2e^{-2x} +3e^{-3x} + \ldots)$
fronthem
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How To add or subtract two numbers from an interval that theree result must be in same interval

I have a question. I'm searching for two methods that 1) Sum of two random numbers from an Intervals must be on that interval. 2) subtract of two random numbers from an Intervals must be on the interval. For example : Interval :[2,6] if randomly…
Mehrdad
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Double summation.

I'm in the middle of an assignment, and I'm not looking for too much help, just more of a push in the right direction (as I haven't really encountered this in my mathematics courses before). I'm looking at Weyl's dimension formula, and I have to…
Jack
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Summation transformation formula(s)

According to this link $$ \sum\limits_{k=j}^{i+j} (j+i-k) $$ is $$ \sum\limits_{k=1}^i (k) $$ Can someone write the Sum formula(s) which was used in this transformation?
pierre
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Does this hold: $\sum_{n=1}^{m}nr^{n}-r\sum_{n=1}^{m}nr^{n}=-mr^{m+1}+\sum_{n=1}^{m}r^{n}$

$\sum_{n=1}^{m}nr^{n}-r\sum_{n=1}^{m}nr^{n}=-mr^{m+1}+\sum_{n=1}^{m}r^{n}$ ,where $n,m$ are integers. Is it true? If yes how to show it? Thank you.
Silent
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How can I compute this sum?

I want to calculate the summation $$\sum_{i=0}^{\log_2 n - 1}\frac{1}{\log_2 n-i}$$ when $n$ is a power of $2$. Even a reasonable estimate on lower bound and upper bound on this summation is fine for me. I know that we can establish the lower…
Subodh
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evaluate $\sum_{i=0}^n \frac {i^c}{2^i}$

I want to evaluate the sum : $\sum_{i=0}^n \frac {i^c}{2^i}$ , when c is some positive constant also could you show the way to compute it ? could any one provide way to compute it when c=1 or other value if could not compute the original one !
Fayez Abdlrazaq Deab
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Tricky Sum of a Hypergeometric Series

I'm finding sums of hypergeometric series quite tricky. I'm see some work done that involve Laguerre polynomials: Sum involving the hypergeometric function, power and factorial functions Here's the…
apg
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Find sum of $\sum_{n=1}^{\infty}\frac{14}{49n^2-84n-13}$ series

$$\sum_{n=1}^{\infty}\frac{14}{49n^2-84n-13}$$ my steps were: $\sum_{n=1}^{\infty}\frac{14}{49n^2-84n-13}$=$\sum_{n=1}^{\infty}\frac{14}{(7n+1)(7n-13)}$=$\sum_{n=1}^{\infty}\frac{1}{7n-13}-\frac{1}{7n+1}$ I was trying count if n=1,n=2,n=3,n=4 and…
Akane123
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Adding up unsetly many real numbers

For example, what is the sum of $[0, 0, 0, 0, ...]$ with as many 0's as ordinal numbers? Is it 0, because I am adding up 0's and nothing else? Here is my way of adding up unsetly many numbers: Take the supremum of the sums of all initial segments of…
3-1-4-One-Five
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Summation Problem

It is given in the question that d|k means d is a positive of k. But, what does that mean? Please just give an answer for this because rest I have to try it out myself.
Rajath Radhakrishnan
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How to rearrange alternating harmonic series to get sum of 1

How can we rearrange $$ \sum \frac{(-1)^n}{n} $$ to get the sum 1 I know we know the alternation of sum by$$\frac{1}{2}\log{k}$$ Edit:sorry forgot to include $$k=a/b $$ a is number of positive terms taken b is number of negative terms taken If we…
unknown user
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Generalised Toloza sum

In 2007 J.C. Toloza discovered a new formula for $\pi$: $\textstyle2+{2\choose2}^{-1}+{3\choose2}^{-1}-{4\choose2}^{-1}-{5\choose2}^{-1}+{6\choose2}^{-1}+{7\choose2}^{-1}-\cdots=\pi$ Toloza's formula essentially relates $\pi$ to one diagonal of…
tywebb
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