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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The mean deviation of a function on independent trials

I have a function f(x). I do M runs and M tends to infinity. For each run, I generate two random samples from the domain of f and calculate the square of the deviation. The image might help clarify. Equation What I have found is that the…
saiftyfirst
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How to compute the summation of this sequence

The sequence is $$ \sum_{i=1}^n i^2$$ I used to know how to do this, but I just forget.
Dylan Zhu
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A little curiosity about sum notation

In summation notation($\sum$), can the stopping point be smaller than the starting point? For example, can I say $$\sum_{i=1}^0 i = 0$$ because $\ 1 > 0$ so it does not sum anything??
Ryan Ro
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Showing a series is some range

Hello I am having some issues trying to show the following series is in the range between 60 and 150 I have to use a non-integral method to show the following. $60 \leq \sum_{n=1}^{32} \lg(k) \leq 150 $ Also I am not allowed to actually evaluate the…
Delta Hex
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How to calculate the number of repayments for a mortgage

Given the principal sum P, the interest rate r, and the repayment M. What is the formula for the number of repayments n?
R. Doolan
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Double summation squared

I need to calculate $(\sum_i \sum_tx_{i,t}-1)^2$. I know that $$ \sum_i \left(\sum_t x_{i,t}-1 \right)^2 = \sum_i\left(2\sum_t\sum_{u>t}x_{it}x_{iu} - \sum_tx_{it} +1\right) $$ from the common square of a sum, and normal binomial formula, but I'm…
Robinbux
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basic sum transformations

I am new to math and I've a lot of problems in basic transformations of equations. For example this one: $$ {n^n}-\sum_{k=1}^n {n \choose k} {(-1)^{k-1}n^{n-k}} = \sum_{k=0}^n {n \choose k} {(-1)^{k}n^{n-k}} = (n-1)^n$$ I don't know how $n^n$ will…
fast-forward
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Is the $\sum_{i=1}^{k} \frac{1}{k+1-i}$ equal to the Harmonic Series when $\lim_{k\to \infty}$?

It is like starting the summation of the Harmonic Series but from the "end".Could we say that when $\lim_{k\to \infty}$ $\sum_{i=1}^{k} \frac{1}{k+1-i}$ is equal to the Harmonic Series?
sliiime
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Interpreting a less than sign after summation

I am trying to interpret an equation, but can't understand how the less-than signs work: $\sum _{n=1}^{\infty } \frac{1}{n^2}<1+\sum _{n=1}^{\infty } \frac{1}{n (n+1)}=1+\sum _{n=1}^{\infty } \left(\frac{1}{n}-\frac{1}{n+1)}\right)=1+1=2$ The first…
Squan Schmaan
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Trouble understanding why $\sum_{i=1}^n i$ = $\sum_{i=1}^{n/2} i+(n-i+1)$

I am reading Steven Skiena's Algorithm Design Manual, trying to review summation in chapter 1.3.5. Skiena states "The sum of the first n integers can be seen by pairing up the ith and (n − i + 1)th integers" and then shows the following two…
Jordan
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Double Series Identity

Show that $$\sum_{k=2}^n (-1)^k \sum_{j=1}^{k-1} a_ja_{k-j} = \Bigl(\sum_{k=1}^n (-1)^ka_k\Bigr)^2 - \sum_{k=n+1}^{2n} (-1)^k \sum_{j=k-n}^n a_ja_{k-j}$$ Source: Determine whether $\sum_{k=1}^\infty\sum_{j=1}^{k-1}\frac{(-1)^k}{[j(k-j)]^p}$…
S10000
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Find $\sum_{r=n+1}^{\infty} \left(\frac{1}{r}-\frac{1}{r+1}\right)$

Find $$\sum_{r=n+1}^{\infty} \left(\frac{1}{r}-\frac{1}{r+1}\right)=\sum_{r=1}^{\infty} \left(\frac{1}{r}-\frac{1}{r+1}\right)-\sum_{r=1}^{n} \left(\frac{1}{r}-\frac{1}{r+1}\right)\;.$$ I found that: $$\sum_{r=1}^{n}\left(…
Jamminermit
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Summation of expression with two variables?

I know of the arithmetic series but I do not think this can be applied here. I have the expression $((j \cdot k)^2k + (j \cdot k)^2j)$. Is there any way to simplify/compute $$ \sum_{j_1 = 1}^{j}{\sum_{k_1 = 1}^{k}{((j_1 \cdot k_1)^2k_1 + (j_1 \cdot…
That Guy
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What is the result of $\sum\limits_{n=1}^{\infty}(n-1)(\frac{5}{6})^{n-1}$?

In wolfram alpha it says it's 30 but I cannot figure out why.
Yuval Rado
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Solving for a function inside a finite summation

I trying to solve for a function inside a finite summation and haven't been able to find many resources on the topic. Below is the general form of the equation and I'd like to rearrange it so solve for the function $f(n)$. It seems like there…
brad14
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