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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Find a formula for $\sum\limits_{r=1}^{n} (r^2+1)(r!)$

The sum $$\sum\limits_{r=1}^{n} (r^2+1)(r!)$$ is equal to: $(n+1)!$ $(n+2)!-1$ $n\cdot(n+1)!$ $n\cdot(n+2)!$ My work. I tried to solve this problem by converting $(r^2+1)$ in squares then applying the property but i was unable to get the…
Himanshu Shekhar
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Find the sum or value of following expression

In the problem I am not able to derive difference term. I know for solving summation we have to make difference term. How to proceed with this problem? $$\frac{{\displaystyle \sum_{n=1}^{99}} \sqrt{10+\sqrt{n}}}{{\displaystyle \sum_{n=1}^{99}}…
mathophile
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Trying to understand to equal sums.

Why is it that? $$z + \sum_{2 \le k \le n}^{\infty} \frac{q^{n-1}}{n-1} k(k-1)p^{n-k} \dbinom{2n-k-2}{n-2}z^n = \sum_{j, k \ge 0}^{\infty} \frac{q^{j+k-1}}{j+k-1} k(k-1)p^j \dbinom{2j+k-2}{j}z^{j+k}. $$ I get that you can just plug $j+k=n$, but…
user528867
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Geometric sum with squared exponentials

Is there a closed form of the following finite sum? $$ \sum\limits_{n=0}^{N}q^{n^2} $$ where $q>0$. The only thing I found somehow related is the Jacobi $\theta$ elliptic function, but there it is an infinite sum.
Joshhh
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Don't Understand Double Summation with Gauss's formula

So as we know, if we have a summation from $1$ to $n$, the simple formula is $$\sum_{i=1}^n i=\frac{n(n+1)}2.$$ But if we have two summations, one from $i=1$ to $n$ and another one $j>i$ to $n$, the formula we get…
reVolutionary
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What is this mathematical expression?

I am trying to figure out what the attached picture's mathematical expressions mean. We have a kernel function $k$ that takes in 2 vectors that are $\in \mathbb{R}^d$. I don't understand what the subscripts in the sum mean, could someone explain?…
24n8
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Approximation of sum $\sum_{j=1}^{n-1}\frac{2j}{(n-j+1)(j+n)}$

I'm trying to solve this sum or at least give an approximation. $$\sum_{j=1}^{n-1}\frac{2j}{(n-j+1)(j+n)}$$ This was my attempt: Assuming that in my sum $\sum f(j)$, $f(j)$ is a monotonically increasing function, then I can approximate the sum by…
Kevin López
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summation question simple

when you are checking to see if a sum of say $k^2$ from $k=1$ to to $k=n$ is equal to a sum of $(k+1)^2$ from $k=0$ to $n−1$ can someone explain what is going on here. THanks (looking for a fairly simple way to work the problem without writing out…
Carlos Bacca
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Empty Range in Multiplication

Why is the following true? $$\prod_{i=6}^2 3^i = 1$$ I can't quite wrap my head around it. I understand that $$\prod_{i=1}^k 3^i = \underbrace{3^1 \cdot 3^2 \cdots 3^{k-1} \cdot 3^k}_{3^{\sum_{j=1}^k}}$$ Is it because that sum is now zero and $3^0 =…
hh32
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How to find if this summation equals zero?

For every value of $n_1$ i tested with, it came out as $0$. However I have no idea how to prove if it does or not for every value of ${n_1}$. Note that ${n_1}$ has to be smaller than ${n_0}$ in the summation. $$\sum_{i=1}^{n_1}…
Eduard
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Find the exact value of $n$ if $\sum_{r=1}^{n}{\ln(\frac{r+1}{r})}=8$

Find the exact value of $n$ if $$\sum_{r=1}^{n}{\ln(\frac{r+1}{r})}=8.$$ So the sum is equal to $$\sum_{r=1}^{n}{\ln(1+\frac{1}{r})}=8.$$ $$\therefore\ln(1+1) + \ln(1+0.5)+...\ln(1+\frac1n)=8,$$ so $$(2)(1+0.5)...(1+\frac1n)=e^8$$ But I am unsure…
H.Linkhorn
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When is the sum non-zero?

Is there an easy way to show that the following expression is non-zero only for $l=1$? $$\sum_{k = 0}^{l} \binom{l}{k} \binom{\frac{1}{2}\left(l + k - 1\right)}{l} \frac{1 + (-1)^{k+1}}{k+2}$$
John
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How to work with sums? $\sum$

During high school I missed out on some of the math lessons due to health issues, one thing I missed out on was working with sums. I am now a second-year engineer student and I am still amazed how bad I am at this. I am reading a math course right…
J. Doe
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Concatenate 2 numeric values to a fixed size number

Let's say you have 2 numbers. First number is always 6 digits long. Second number can vary between 1 and 4 digits. If it's less than 4, it has to be padded with 0. The end result always needs to be 10 digits. Example #1: n1 = 111111 n2 =…
HABJAN
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How to evaluate or model summation equation

This is a basic question on the meaning of the following notation. Can someone explain how I would evaluate the Summation forumula below? And perhaps point me to a reference where I can understand how to evaluate? I am assuming that we are trying…
StudentAP_2022
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