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.

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Product of Summation for a single table of values.

I've been looking around but can't get a exactly clear answer on my question. I'm provided a table of values of $x_i$ and $y_i$ for $i = 1$ to $i = 5$. I'm then asked to evaluate $$\sum_{i=1}^5\sum_{j=1}^5x_jy_i$$ I know that they're recognised as…
Anthony S.
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Simplify a sum of n products

Given the following sum formula: $\sum\limits_{i=1}^{n} (i\cdot 2^{n-i}) $ Can you help me out to a simplify the formula and provide an formula without a Sigma sign? I know that I cannot just split the Sigma like that: $\sum\limits_{i=1}^{n}…
Stasel
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Minkowski sum of two Objects

I'm trying to implement the ClearPath pathfinding algorithm, that relys on velocity obstacles. It is assumed, that both objects have a circular hull. However, I do not understand how to calculate the minkowski sum of two objects. Here's an excerpt…
PAThePianoDude
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Partial sum of $\sec nx$

Does there exist a closed form of $$\sum_{n=1}^n \sec nx$$ that is expressed in elementary terms? $${}{}{}{}{}{}{}{}{}{}{}$$
John Glenn
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Equivalent summations

If the function $p(r)$ maps from the positive integers to the non-negative real numbers and has the property that $\sum_{r=1}^\infty p(r) = 1$, and $x_1, x_2, ... x_n$ is a sequence for which $X = \sum_{r=1}^\infty x_r p(r)$ is well-defined and the…
sanjayr
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Summation rules and properties

I am trying to find the sum of this - $$\sum_{r=1}^{100} ( 1 + 2r + 0.3^r ) $$ I know roughly how I am supposed to do. First I distribute the summation across the 3 values. Then I got stuck $2r$ and $0.3^r$ Both are similar if I understand, so I…
user185692
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Closed form of an expression.

I want to show $\dfrac{1}{\pi}\sum_{m=1}^{\infty}\dfrac{\sin(2\pi mx)}{m}= -(x-[x]-\dfrac{1}{2})$,when x is not an integer,where [x] denotes greatest integer function . Could you please give any suggestion how to approach?? Thanks
Hitendra Kumar
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Finding the answer of a summation

Let $\sum_{i=1}^{n}g(x_{i}) = G$. What is important is that I do't know the value of $g(x_{1}),...,g(x_{n})$, and I only know the value of their summation. How I can compute the answer of the following summation based on $G$ …
Hasan Heydari
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Nested summation with varying limits

I have a function: $$\rho(i,j)\ \ \ \ \textrm{for}\ i=1,\ldots,n\ \textrm{and}\ j=1,\ldots, m$$ I can write a summation $\rho(i,j)$ for all values of $i$ and $j$: $$ \sum_{i=1}^n \sum_{j=1}^m \rho(i,j) $$ How can I write this summation if m is not…
bem
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Can i simplify following math expression?

I have following expression: $\left\lfloor\frac{n}{10}\right\rfloor+\left\lfloor\frac{n}{10^2}\right\rfloor+\left\lfloor\frac{n}{10^3}\right\rfloor+\ldots+\left\lfloor\frac{n}{10^{\lfloor\log_{10} n\rfloor}}\right\rfloor$ where $n$ is a positive…
blindProgrammer
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Difference between Summation and Sn

What is the difference between $\Sigma $ and $ S_n $ Can they be used interchangeably? If not then when can they be interchanged?
William
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Is it possible to infer $v$ from divided summations?

I have a problem. I worked on it for some time and I've got this: $$\frac{\sum_{k=0}^{n/2} v^{2k}}{\sum_{k=0}^{n/2} v^{2k+1}}=\frac{1}{2}$$ The only thing we know about $n$ is that it is even. Is it possible to infer $v$ from this? If not, I guess…
Hanlon
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How to exchange this double sum?

I have a sequence of sets $D_i$, and currently the sum is $$\sum_{i=1}^n \sum_{d\in D_i} 1 $$ How would I exchange the sum so that we run through $i$ first?
ColosseumsGra
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How to formally show that following summation is equivalent?

In on of the book I read that $$\sum_{i=1}^{2k+1}\sum_{m+n=i+1}Y_{mn}t^{i-1}=\sum_{m,n}^{k+1}Y_{mn}t^{m+n-2}$$ where $Y_{mn}$ is the $(m,n)th$ entry of symmetric matrix (of size $k+1$) and $t$ is some constant value from the real set. Here is my one…
Frank Moses
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Summation question basic

After solving a probability question I ended up with the following: $P(A)=\frac{1}{6}\sum\limits_{n=1}^\infty(\frac{5}{6})^{3n-2}$ limit between 1 and infinity but I'm unsure how to carry this on , I am familiar with summing $x^n$ to infinity for…
user528906
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