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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what does this summation $\{q>p\}, \{p\}$ mean?

$$ \frac1{(T-t)A_0^2\Delta}\sum_{\{q>p\}, \{p\}}\frac{\tau_p^{z_1-1}}{\Gamma(z_1)}\hat u(t_q-t_p-1)\frac{\tau_q^{z_2-1}}{\Gamma(z_2)} $$ Hi, can anyone help me with this summation? does $\{q>p\}, \{p\}$ mean $(p=1, q=2, 3, 4...) + (p=2, q=3, 4,…
Hsin-Yen Lee
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Problem with understanding notion of symmetric sums

I can write out the symmetric sum of for example $x^1_1x_2^2x_3^3$ but I don't understand the notion of $\sum_{sym}x{^1}_{\sigma(1)}x{^2}_{\sigma (2)}x{^3}_{\sigma(3)}$ where $\sigma$ runs over the permutation {1,2,3}. Specifically I don't…
per persson
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Show these two equal each other

I can show that $\sum(Y_iX_i) - \bar{Y}(\sum X_i) $ is equal to $\sum(Y_i - \bar{Y})(X_i - \bar{X})$. I cant, however seem to go from the LHS to the RHS or at least make it make sense to myself. It was suggested that I add zero by adding and…
Andrew Igdal
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How can I rationalise a few numbers to restrict their sum to a particular value in excel?

For example: i have the following numbers whose sum is 46. 5 3 4 4 30 I need their sum to be restricted to 40. I need to now rationalise/ normalise the set of 5 numbers so that their sum does not exceed 40. Can you help me with a formula that…
Noor
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Minimum value of $\sum_{1\le i \lt j \le 2022} a_ia_j $

Hello how can I find the minimum value of $$\sum_{1\le i \lt j \le 2022} a_ia_j $$ Where $ a_i $ and$ a_j $ are -1 or 1? My thought was that the number of -1 and 1 (so 1011 -1's and 1011 1's) should be same but I'm not sure if that is right.
주성우
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If $\sum_{k=1}^n (2k-1)a_k = n(n+1)(4n-1)$, find $a_n$

I'm not getting any idea what to do with this problem. If given that $\displaystyle\sum\limits_{k=1}^n (2k-1)a_k = n(n+1)(4n-1)$ then how can we find out $a_n$. I need some hints to start.
user983440
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Simplify Triple Sum — Einstein Summation Notation

Schaum's Outline to Tensor Calculus — Chapter 1, Solved problem 1.5 — Use the summation convention to write and state the value of $n$ necessary in: $$g^{\LARGE{1}}_{11} + g^{\LARGE{1}}_{12} + g^{\LARGE{1}}_{21} + g^{\LARGE{1}}_{22} +…
Dwayne E. Pouiller
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Problem with sum (contains a binomial)

I need to calculate the following sum: $\sum_{x=0}^y x\binom{y}{x}\alpha^x(1-\alpha)^{y-x}$ i know it equals: $\alpha y$, but I don't know how to calculate it exactly. My steps: $\sum_{x=0}^y x\binom{y}{x}\alpha^x(1-\alpha)^{y-x}=\sum_{x=0}^y…
John
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Matrix summation across one axis or dimension

I have a matrix $A_{w,x,y,z}$ and I want to show average across the w axis. So I want my new matrix $X$ to be of shape (x,y,z) since we too the mean across w. What is the proper way to write this in LaTeX notation. $\sum\limits_{n=1}^{w}…
amstergc20
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Converting expression to summation

Apologies but I am having difficulty understanding how to convert a simple expression to a summation. I have three parameters: x = final rating y = major criteria z = minor criteria The final rating is the sum of the major criteria (which is…
jim
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Is this summation formula true?

Show that $$\left(\sum_{j=0}^n x_j\right) + x_{n+1} = \left(\sum_{j=0}^{n-1} x_j\right)$$ It's not obvious to me that the two are equal. It seems that the left side goes up to $n + 1$ whereas the right side goes up to $n - 1$.
Andrew
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Evaluating $\sum_{i=0}^{\log_2(7)} 2^i$. What am I doing wrong?

I was working with summations and I stumbled upon a sum that I could not reconcile: $$\sum_{i=0}^{\log_2(7)} 2^i$$ Using the formula $$\sum_{i = 0}^{n} x^i = \frac{x^{n+1}-1}{x-1}$$ found in a university textbook, with $x = 2$ and $n = \log_2(7),$ I…
Linnea117
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An upperbound on a frequencies problem

I've this problem: Given a a list of frequencies $f_1 \geq f_2 \geq ... \geq f_n $ of $ n $ elements, such that $ \sum_{i=1}^n f_i = m $ where $ m $ is a multiple of $ n $. Prove that $ \sum_{i=1}^n i f_i \leq \frac{m(n+1)}{2}$. Now I've proved…
Pur2all
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Writing a formula using summation/sigma notation

I seem to be having a problem with writing a general sigma notation for my case. In this example, I am trying to sell a product on multiple markets (based on the customer's needs), but for each market the customer chooses, he shall get an additional…
lukascobbler
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Calculating the series $\ln(1+x)$ using polynomial

Calculating the series $\ln(1+x)$ using polynomial Here's what I have tried $$\begin{align*} (1+ax)\ln(1+x) &= \sum_{n=1}^{\infty} (-1)^{n-1}\frac{x^n}{n}+a\sum_{n=1}^{\infty} (-1)^{n-1} \frac{x^{n+1}}{x^n} \\ &= x+…
joe_bill.dollar
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