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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Radius of convergence for a given sum

What is a brief description of the radius of convergence? How do you find the radius of convergence for $$\sum_{i=1}^{\infty}2^i\cdot x^{-3(i-1)}$$
user117520
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Infinite sum with infinite poles

I want to evaluate the sums $$ \sum_{q=-\infty}^\infty\frac{1}{\sin\left(a q + x\right)\left(q + b \right)^4} $$ and $$ \sum_{q=-\infty}^\infty\frac{\cos\left(a q + x\right)}{\sin^2\left(a q + x\right)\left(q + b \right)^3} $$ where…
Mike
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Summation Indices - How to interpret the zero index?

A very quick background - I'm a programmer by trade that has decided to try and properly relearn the math I never fully grasped 10 years ago in school. I can "perform calculations", and am rather proficient at fortran, but at no point would I ever…
penland365
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Sum to infinity - sector

How would I start this question?
Jim
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Are these two summations equivalent?

Is $\sum_{y=2}^{\infty} (\frac{1}{y})(1-p)^{y-1}$ equivalent to $\sum_{y=1}^{\infty} (\frac{1}{y})(1-p)^{y}$ ?
pyler
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$\sum^n_{i = n+1} 1$ is $0$ or underfined or identity element for the operation it's in?

Let's say you have the $\sum^n_{i = n+1} 1$. The things to add don't exist, because $n+1 > n$. What do you do then? Do you count it as $0$? Because $0$ is the identity element for addition? What if it was multiplying from $n+1$ to $n$? Would that be…
user3577958
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finite sum of powers

Can you find what $\sum_{i=1}^{n}\left(n/i\right)^{i}$ is equal to? By simulation, I know that a loose upper bound is $2^n$. I am happy with a proof of such upper bound if an exact expression is not available.
Student
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Question about a sum

Why is it that $$\sum_{k=1}^n(n+k+1)(n+1)=\frac{3}{2}\sum_{k=1}^n3k^2+k.$$ I cannot understand it. This is not homework, I am just a little interested in this!
Patrico
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Sum of positive integers

Find the sum of all positive integers x less than 100 for which (x^2)-81 is a multiple of 100? To do this manually would be too tedious. Also, can someone explain what the latter part of the question is saying?
user140161
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Algorithm for summing all subsets?

Given a set of integers, is there an algorithm that returns the sum of all the subsets? For example if $s = \{6, 3, -2\}$ then the algorithm returns $28$. I.e: $$(-2) + (3) + (3-2) + 6 + (6-2) + (6+3) + (6+3-2) = 28$$ The runtime of this is…
C Shreve
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Prove by induction:$\sum_{i=0}^n 3^i = \frac {(3^{n+1})-1}{2}$

Prove by induction: $$\sum_{i=0}^n 3^i = \frac {(3^{n+1})-1}{2}$$ Basis: For $n=0$ we have $1 = 1$ Inductive Step: Now this is where I don't know what to do, any kind of help would be much appreciated. Thanks!
Harvat
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O(1) Exponential summation

Is there an O(1) (uses a function instead of summation/for loop notation) way to calculate $$ \sum\limits_{i=0}^n x^i $$ Given (x,n) Example: (4,3) 64+16+4+1 (3,3) 27+9+3+1 (2,10) 1024+...+8+4+2+1 I know that for x=2, f(x,n)=(x^(n+1))-1 I am in…
Starfy_S
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How find the $\sum_{n=0}^{\infty}\frac{(2n-1)!!}{(2n)!!}\cdot\left(\frac{1}{2^n}\right)$

Find the sum $$\sum_{n=0}^{\infty}\dfrac{(2n-1)!!}{(2n)!!}\cdot\left(\dfrac{1}{2^n}\right)$$ we know $$(2n-1)<2n$$ so $$\dfrac{(2n-1)!!}{(2n)!!}\cdot\dfrac{1}{2^n}<\dfrac{1}{2^n}$$ so this sum is converge I think use $\arcsin{x}$,But I can't,Thank…
math110
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If $\sum a_i+\sum b_i>\sum a_i$, is it possible to show that $\sum a_i^k+\sum b_i^k\geq \sum a_i^k$?

Another probably stupid question of mine: For real $a_i$'s and $b_i$'s: If $\sum a_i+\sum b_i>\sum a_i$, does it follow that $\sum a_i^k+\sum b_i^k\geq \sum a_i^k$, $k\geq 1$ and if so how can it be shown? It should be noted, that all the $a_i$'s…
john stepanov
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Summation rules and help

If i had a situation like, $$\sum^{N}_{i}B_{i}\times \frac{\sum_{i}^{N}|A_{i}|}{\sqrt{\sum^{N}_{i}(A_{i})^{2}}}=0 $$ I am struggling to see how it can be rewritten in a simpler form, I have tried expanding the the sqrt about zero but that gets very…
user3261646
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