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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Nested sum with dependent summation variables

The following identity involves a reversal of order of summations. It seems to be correct when I tried through some examples. The sagecell code for verifying some examples is here. But how to give a proof for this?…
Vishnu Namboothiri K
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Simplifying a finite summation expression.

I found a question that asks to evaluate the following expression: $\frac{1}{\sqrt4 +\sqrt5} + \frac{1}{\sqrt5 +\sqrt6} + \frac{1}{\sqrt6 +\sqrt7} + … + \frac{1}{\sqrt{624} +\sqrt{625}}$ I was able to represent the above expression in summation…
FireTheLost
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Help finding when a summation is greater than $1$.

Just a quick question. Not sure if I have all the tools to solve this and I'm looking for a little direction. I'm looking at the following summation $$\sum_{i=1}^{n} (1 - x_{i})$$ I know that $0 < x_{i} < 1$ for all $i$. Is there a way to tell when…
Tiny Tim
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How to write this in summation notation $f^0(k^n)+f(k^{n+1})+f^2(k^{n+2})+f^3(k^{n+3})+\dots +f^{n+p-1}(k^{n+p-1}) $?

I have function $f$, where $f^n$ denotes composition and $0
stephan
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Showing that switching the order of variables gives same sum so as to simplify the required expression for exact sum

If $S(x,y)$ = $\sum_{y=0}^{\infty}$$\sum_{x=0}^{\infty}$$\frac{(x+y +xy)}{(5^x(5^x +5^y))}$ , then if we want to show that $S(x,y) = S(y,x)$ so as to get the simplification by adding both to get the exact sum . I tried to evaluate…
Paracetamol
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Finding triple sum of the dependant variables method checking

Find: A) $\sum_{i \geq j \leq k} \frac{1}{3^i 4^j 5^k}$ $i,j,k$ vary from $[0,\infty)$ B) $\sum_{i
Paracetamol
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Equality of sum of multiplications with the same factor

Suppose I know that the following equality holds: $$ \sum_{x} A(x)C(x) = \sum_{x} B(x)C(x) $$ Can I conclude that: $$ \sum_{x} A(x) = \sum_{x} B(x) $$
Gilberto Cunha
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shifting summation index

How would one shift the summation index to combine like terms in this expression? I am finding this concept very confusing for some reason. $\phi_{h}(z-z') + \sum^{\infty}_{n=0}[W^{n+1}_{TS}\phi_{h}(z+z'-2(n+1)h) + W^{n}_{TS}\phi_{h}(z+ z'+2(n+1)h)]…
ConsistentC
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Infinite Summations and Products in the Extended Natural numbers

I know that this isn't a normal constraint but let's say we are working with the standard Von Neumann Naturals $\mathbb{N}$ within ZFC and not some arbitrary system. So no results from $\mathbb{R},\mathbb{Z}, \mathbb{Q}$ are applicable. Now lets get…
Pymamba
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Limit of sum $\sum_{x=1}^{\infty} \frac{1}{\sqrt{x}\sqrt{x+1}}$

I am having a hard time proving if this sum converges or diverges: $$\sum_{x=1}^{\infty} \frac{1}{\sqrt{x}\sqrt{x+1}}$$ I tried proving it by the ratio test but $q = 1$. I couldn’t proceed further and would like some help.
jophny
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Converting simple code to a math expression

I am curious if there is a way of somehow recreating such code as a math statement. S = [1,2,3,4] output = 0 for x in S: N = S.copy() N[x-1] = 0 for y in N: output = output + y The only thing that I could think of is…
abno525
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A summation formula where I have trouble to find the priorities of its calculations

I'm unease with summations and their priorities. I'm stumbling upon this, on a book: Am I : correctly reading this, here : $$ \text{MSI} = \sum\limits_{i}\Bigg[\frac{\Bigg(\frac{p_{i,j}}{\sqrt{\prod\limits_{i}{a_{i,j}}}}\Bigg)}{n_{i}}\Bigg]…
Marc Le Bihan
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What rule is being applied to justify this summation equality?

In computing a sum, my book writes $$\sum_{7\leq k^2\leq 45} \frac{1}{k} = \sum_{\lceil \sqrt{7} \rceil \leq k \leq \lfloor \sqrt{45}\rfloor} \frac{1}{k}$$ How did they do this? I'm not looking for a proof that the two sums are indeed equal, I'm…
user236343
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Algebra and Substitution in Quadratic Form―Einstein Summation Notation

Schaum's Outline to Tensor Calculus ― chapter 1, example 1.5 ――― If $y_i = a_{ij}x_j$, express the quadratic form $Q = g_{ij}y_iy_j$ in terms of the $x$-variables. Solution: I can't substitute $y_i$ directly because it contains $j$ and there's…
Dwayne E. Pouiller
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Is there a name for the polynomials which give pure powers of n when summed to n?

For context, I'm an A Level student (16 years old) but I have a passion for mathematics and do a lot of it in my spare time. I found an interesting question in an A Level textbook a while ago that asked for polynomials $f_2(r), f_3(r)$, and $f_4(r)$…
DoctorDalek
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