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 & Average: Latex formatting

I want to describe the following scenario mathematically. I think I have it right... Just wanna check! Lets say we take a reading A. We then take a number of readings (R) (n readings). We then calculate the difference between each reading & A. We…
user114381
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In the process of proving Sum of Geometric Progression

I was reading the proof for the sum of geometric progression at http://www.proofwiki.org/wiki/Sum_of_Geometric_Progression and one of the statements is the…
Alby
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formula to sum discounting cash flows

Is there a formula that can perform this discounting of a constant cash flow to present value without having to do the whole summation? $$DCF=\dfrac{CF_1}{(1+r)^1}+\dfrac{CF_2}{(1+r)^2}+\cdots+\dfrac{CF_n}{(1+r)^n}$$ As you can see; currently I…
Raynos
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Summation of $\sum\limits_{j=2}^n (j-1) = \frac{n(n-1)}{2}$

In the summation: $\sum\limits_{j=2}^n (j-1) = \frac{n(n-1)}{2}$ Given that $\sum\limits_{j=2}^n (j) = \frac{n(n+1)}{2}-1$. Expanding it: $ \frac{n(n+1)-2n(n+1)}{2}$ = $ \frac{-n(n+1)}{2}$ and bringing the minus sign inside $ \frac{n(n-1)}{2}$. So…
user112780
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What is this formula called? summation

Does people know what this formula called? I want to google its properties and read about it more - if it has official name
ERJAN
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Simplifying an Expression Involving a Summation

Can anyone think of a way to simplify $$ \sum_{k = 1}^n \left[ 1 - \left(\frac{n - 1}{n}\right)^{k - 1} \right] $$ to a more elegant expression? I've been trying to tweak it using the binomial theorem after expanding it but it's just looking uglier…
Jamie Sethian
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With $z_y = y!+2$, find $\sum_{i=3}^3 z_i$

I'm lost on the factorial included here in this problem. Any help is appreciated! sequence is $z_y= y! +2, Y \ge 1.$ Find $\sum\limits_{i=3}^3 z_i$.
tony
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Infinite sum $\sum_{n=1}^\infty{\frac{1}{n2^n}}$

How do I evaluate this sum: $$\sum_{n=1}^\infty{\frac{1}{n2^n}}$$
user1510374
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How to go about calculating this finite summation?

I have the summation $$ \sum_{n = 0}^{10} \frac {1 + (-1)^n} {2^n} $$ I have looked up how to work out sequences without manually finding each term and adding it up, but I have only found out how to work out problems like $n^2$, $n^3$, etc. How…
Maria
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How to reduce function

I'm dummy in mathematic, but in the Universite I got an exercise to write in C++ graphic of this mathematical expression: $$ \sum_{k=0}^{\infty} (-1)^{k+1}\frac{x^{2k}}{k!} $$ where $x\in (-10,10)$. So, I dont know how to calculate it. But of…
okonik
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how do I compute this summation of the expected value

How do I compute the summation at the end: $$E(x) = \sum_{x=1}^\infty x.P(X=x) = \sum_{x=1}^{\infty} x \left(\frac{5}{6}\right)^{x-1}$$
Joyce
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Evaluating Sums $\sum_{i=1}^{n} \sum_{j=0}^{n-i}$

I'm unsure how to evaluate sums when the second sum has $n-i$ on the top. $$\sum_{i=1}^{n} \sum_{j=0}^{n-i} (3j^{2} - 2)$$ $$=\sum_{i=1}^{n} (\sum_{j=0}^{n-i} 3j^{2} - \sum_{j=0}^{n-i}2)$$ $$=\sum_{i=1}^{n} (\sum_{j=0}^{n-i} 3(\frac {n(n+1)(n+2)} 6…
GivenPie
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How to calculate $\sum_{i = 0}^{k-1}\left(\frac{5}{6}\right)^i$

I need to calculate the complexity of an algorithm. I have come across this summation that I can't evaluate, I am stuck. I haven't seen one of those in years, therefore I am rusty and really struggling: $$\sum_{i =…
haunted85
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Changing index of summation. $\sum_{y=1}^\infty (1-\theta)^{y-1}\theta$

I am always confused how to change the index of summation. $$\sum_{y=1}^\infty (1-\theta)^{y-1}\theta$$ The above is supposed to be a geometric sum and sum up to $1-(1-\theta)^x$? But how?
Jiew Meng
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Splitting sum using index notation

Using index notation a sum $S=\sum_{i=1}^{N}a_i b_i$ can be written without the summation symbol since $i$ is a repeated index. Is it possible to write the sum in two terms $$S=a_1 b_1 + \sum_{i=2}^{N}a_i b_i$$ in the same way (by using a Kronecker…
user877329
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