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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Sum of $k^4$ from $0$ to $n$

How can I find this summation? I started by expanding $(k+1)^5$ and setting the summation of both equal to each other. There is some cancellation but I don't know what to do afterwards.
Jesus
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What is mathematical term to describe this confusion?

This is in reference to a question on stackoverflow - https://stackoverflow.com/questions/22445470/getting-more-data-while-converting-data-int-to-float-and-doing-division-and-mult#22445470 The following sql-scripts will generate values below, same…
Vladimir Oselsky
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Why does this equation holds?

Could anyone tell me why following equation holds? $ \sum_{n \geq 0} x^n \sum_{i \geq 0} \binom{i}{n-i} = \sum_{i \geq 0} x^i \sum_{n \geq 0} \binom{i}{n-i} x^i$
cinvro
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How prove this $arg((1+ia)(2+ia)(3+ia)\cdots(n+ia))=\arctan{\frac{a}{1}}+\arctan{\frac{a}{2}}+\cdots+\arctan{\frac{a}{n}}$

let $i^2=-1,a>0$, show that $$arg((1+ia)(2+ia)(3+ia)\cdots(n+ia))=\arctan{\dfrac{a}{1}}+\arctan{\dfrac{a}{2}}+\cdots+\arctan{\dfrac{a}{n}}$$ I can't How prove this equation,Thank you because $n=1$.we have $$(1+ia)=\arctan{a}\Longleftrightarrow…
math110
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Finding rooms of Summation

Hi I was wondering how do I Solve this question. I have to solve for $a$. I can solve for it when there's one summation but now there are three. My guess is factoring out the $A$. Divide $s$ by the $3$ summations $X$ $3$. The constants are…
user3276954
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Difficulty with understanding summations

I am in advance sorry if this question is too easy for this site, but I am having real problem understanding how to solve this summation: $$\sum_{i=1}^n{i*2^i}$$ I understand basics of summations but i don't know where to start, please help.
Filip
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What is the sum of integers from $1$ to $789999$ ? asks the professor

How to resolve it? How to find that sum?
user125265
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Simple addition of summation

I know the following equality holds from previous work $\sum_{i=1}^{n}a_i^2\sum_{j=1}^{n}b_j^2 + \sum_{i=1}^{n}b_i^2 \sum_{j=1}^{n}a_j^2$ = $2(\sum_{i=1}^{n}a_i^2)( \sum_{i=1}^{n}b_i^2)$ But when I set values for the two sets a and b I'm getting an…
user101104
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Sum of phase shifted cosines

I'm trying to prove that $$\sum_{n=0}^N \cos(\pi n/N) = 0$$ when $N$ is large. I could make an integral that basically does the same thing: $$\int_0^N \cos(\pi n / N) dn$$ $$=-\frac{N}{\pi}\left[ \sin(\pi n /N) \right]^N_0$$ $$=0$$ I'm just not…
user2162498
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solving for a single variable in an algebraic summation…that includes exponents in the functions

I feel that I could have solved this in my sleep in high school--but I've been "out of math shape" for too long. I have a team working in Objective C (for an iPhone app), and I gave them the equation (i've written in long form but do have the…
bacchus6
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how to find a sum of numbers in a sequence when some intermediate terms are not taken in to consideration?

How to find $$\sum\limits_{i=1,i\neq 5,12,23,45}^{100} i^3$$ One way I know is $$\sum\limits_{i=1}^{100} i^3-5^3-12^3-23^3-45^3$$ But when the missing terms in the sequence become large it is difficult and time taking to find the sum. Is there any…
Litun
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What would this geometric series' "Common Ratio" be?

$$\sum\limits_{n=1}^∞ (n^2 + \frac{n}{n+3}) = 1\frac{1}{4} + 4\frac{2}{5}+9\frac{3}{6} + 16\frac{4}{7} +25\frac{5}{8}...$$ I can't seem to figure out what the common ratio for this series is, not that it's non-existent, probably just that i'm not…
Sam Chahine
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Summation of power inequalities

some idea for solve (?): $x\in \mathbb{R}$ $\sum_{n=2}^{\infty } x^{n}\le 6$ I am at a loss :/ Thx
studisman
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An equality relating to Mobius function

How $\sum_{n=1}^\infty \frac{\mu(n)x^{1/n}}{n}$ is approximately equals x ? where $\mu(n)$ is mobius function !
Shivanshu
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Summation and exponential problems

Solving $$\sum_{k=0}^\infty \frac{k(vt)^ke^{-vt}}{k!}$$ where v is a constant. How is the answer equals vt?
user107676
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