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 sequences-and-series for sums of infinite series and questions of convergence; use summation for questions about finite sums and simplification of expressions involving sums.

17770 questions

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0 answers

Infinite series

Good afternoon. I'm brazilian, then sorry by my bad english. I have a problem with one question about Infinite Series. I searched for anyone method could help me. I have all constants values (w, y, z, h, a). But I don't know what do. Someone can…

summation

asked Apr 22 '15 at 21:02

Daniel

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1 answer

Do we have $\sum_{n=1}^\infty 0=0$?

Simple question: Do we have $$\sum_{n=1}^\infty 0=0$$ ? Mathematically this seems obvious, but in practice I am very uncomfortable with this. Because nothing is perfect, so $0$ might not be quite zero, say $0.0000000000001$.…

summation

asked Apr 19 '15 at 13:02

user232646

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7 answers

How to derive $\sum_{k=0}^{n}2^{k}(n-k) = 2^{n+1} - n - 2$?

In answering this question, I thought about working out a closed-form formula for $f(n)$ there. I got as far as writing: $$ f(n) = \sum_{k=0}^{n}2^{k}(n-k) $$ …but I wasn't sure how to go farther. I plugged this into Wolfram Alpha and it spat out…

summation

asked Apr 03 '15 at 21:34

Michael Smith

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2 answers

Does $\sum_{n=1}^{x-1}\frac{1}{x-n}$ has a limit as $x \rightarrow \infty$?

Consider the sum $A = \frac{1}{x-1} + \frac{1}{x-2} + \ldots + 1 = \sum_{n=1}^{x-1}\frac{1}{x-n},\quad x > 2$ Can anyone provide some hints on how to proof that the $\lim_{x\rightarrow\infty}A$ exists or not? Initially I thought the sum goes to…

summation

asked Mar 24 '15 at 12:12

Panagiotis Panagi

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0 answers

Growth of exponential sum

i am calculating large data sets with program i wrote and i have two different methods to do this. The first way is to calculate it all at once and the second way to calculate result is to do it in smaller chunks which is faster with short input…

summation

asked Mar 24 '15 at 08:36

tcrat

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1 answer

some questions about interchange summation signs of multi-summation

Besides e.g. $\sum\limits_{b=c}^d\sum\limits_{a=c}^bf(a,b)=\sum\limits_{a=c}^d\sum\limits_{b=a}^df(a,b)$ , are there any further good formulae about interchange summation signs of multi-summation? For…

summation

asked Mar 22 '15 at 11:51

Harry Peter

7,819

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0 answers

double sum with a binary variable of three elements

I have a binary variable $\ v(s,c,h)\ $which takes value 1 if subject $\ s\ $is taught in classroom $\ c\ $in time slot $\ h\ $ and 0 otherwise. I have a question about a type of constraint that I cannot completely understand. For example, every…

summation

asked Mar 05 '15 at 11:37

Vassileios Dermentzis

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3 answers

Sum of powers: $1^m+2^m+3^m+...+n^m$=?

For any positive integer $n$ and $m,$ I was wondering if there is any way to get a closed formula for $$S(n,m)=1^m+2^m+3^m+\cdots+n^m$$ something like $$S(n,1)=1+2+3+\cdots+n=\frac{n(n+1)}{2}.$$

summation

asked Feb 27 '15 at 18:55

mathguy

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0 answers

Double sum to single sum? Simplification.

Can this double sum be simplified to a single sum and further simplified using geometric series? $$\left(\sum_{k=1}^{K} s^{2k+1} \left[T^{2k} E e^{(r)}\right]_\beta \right) \left(\sum_{m=1}^{M} s^{2m} \left[T_2^{2m-1} E_2 e^{(r)}\right]_\beta…

summation

asked Feb 18 '15 at 19:06

Jonathan

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1 answer

Are these equivalent summations?

I just want to ask if $$\sum_{i=1}^n \sum_{j=1}^i |a_i \bar b_j-a_j\bar b_i|^2 = \sum_{i=1}^n \sum_{j=1}^n (a_i \bar b_j-a_j\bar b_i)(\bar a_ib_j + \bar a_j b_i)$$ is true and possibly an explanation on why the summations change from $\sum^n$ to…

summation

asked Feb 10 '15 at 16:33

user214010

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1 answer

Can someone explain why this summation is equal?

Can someone explain to me why this is equal? $$\sum_{i = 1}^n i = \sum_{i = 1}^n (n - i + 1) = \sum_{i = 0}^{n - 1} (n - i)$$

summation

asked Jan 28 '15 at 18:31

kalvin

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3 answers

What does the $i < j$ mean in $ E = -(\sum_{i

This is the energy function that is defined for Boltzmann Machines: $ E = -(\sum_{i

summation

asked Jan 20 '15 at 20:24

Stefan Falk

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1 answer

Evaluation of an Infinite Converging Sum

I was asked to find the value of the following summation. $$ x=1+\sum_{i=1}^{\infty}\frac{1}{2^i}+\sum_{j=1}^{\infty}\frac{1}{3^j}+\sum_{k=1}^{\infty}\frac{1}{5^k} $$ I "solved" it approximately by expanding a few of the terms for each of the…

summation

asked Jan 17 '15 at 01:24

stett

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3 answers

Summation/Sigma Notation Question

This is my first time on here. I am in first year engineering, and I'm having some trouble with sigma notation. Here is the question and answer: I am trying to convert the summation into closed form, using the rules of summation, and the…

summation

asked Jan 13 '15 at 23:40

user2620463

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1 answer

Closed form for this partial polynomial sum? $\sum_{i=0}^{k-1} {n + i - 1 \choose i} x^i$

I came across a sum: $$p_k(x, n) = \sum_{i=0}^{k-1} {n + i - 1 \choose i} x^i$$ and I was wondering if it had a closed form. I found on wikipedia: $$\sum_{i=0}^{\infty} {n + i - 1 \choose i} x^i = (1 - x)^{-n} \text{ for } |x| < 1$$ but it had…

summation

asked Jan 11 '15 at 17:18

DanielV

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