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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How does this summation hold?

How does $$ \sum_{r=0}^{m+n} \left( \sum_{k=0}^{r} \binom{n}{k} \binom{m}{r-k} \right) \ x^{r} = \sum_{r=0}^{m+n} \sum_{k=0}^{m+n} \binom{n}{k} \binom{m}{r} \ x^{r+k} $$ hold? RobJohn helped me, but I could do only this: $$\sum_{r=0}^{m+n}…
Silent
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How should I solve this summation problem?

Lets say that we have these $x$ and $y$ coordinates $x=1,2,3,4,5$ and $y=6,7,8,9,10$ and where $n=5$. How would I use these $x$ coordinates with the first summation? Now, I know that learning is important and it's never a good idea to get other…
Hard Worker
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Sum of eight even integers that cannot be repeated more than twice is $50$

The sum of eight positive even integers is $50$. If no integer can appear more than twice in the set, what is the greatest possible value of one of the integers? This was a question I encountered on an online SAT test, I got stuck on it because if I…
Ali
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Sigma sums problem

Could you please help me with the below result? How do we get from here $(1+2\sum_{j=1}^\infty\rho^j)π_0=1$ To here $π_0=(1-\rho)/(1+\rho)$ Many thanks
user152674
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Calculate simple non geometric sum

I want to calculate this sum. How can I do it ? $$ \sum_{i=1}^n i \cdot \left(\frac{9}{10}\right)^i$$ I know how to calc geometric sum, but how to calc this?
MathDav
  • 556
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3 answers

Solve sum with n and i

I'm struggling to simplify this equation: $$3 + \sum_{i=0}^{n-1} 18n-18i-32$$ Wolfram Alpha tells me that i can simplify this to $3+9n^2-23n$. How ist that possible? Thank you
Bernd Strehl
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Sum with natural log

The sequence $u_n$ is defined by $u_n=0.5^n$ Find the exact value of $\sum_{0}^{10} ln(u_r)$ Is there a common ratio for this? $\frac{ln(0.5^1)}{ln(0.5^0)}$ dividing by 0 not possible..?
Jim
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How to use the summation symbol correctly

I'm absolutely horrible at maths. I'm trying to write out mathematically that for every two minutes in a day a function executes, and this function results in saving x KB of data and y KB of some other data to a computer disk. Now I want to write…
Force444
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Find a number in a set that is not equal to sum of any other numbers

Given a set of nonzero real number S= $\{d_1,\cdots, d_N\}$, can I find a number $d_e \in S$ such that there does not exist $d_m,d_j\in S$ such that $d_e = d_m+d_j$ ? Assume $m$ and $j$ can be equal and $m,e,j$ denote the indices with $e\neq m,j$.
widapol
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How do these two summations equate?

Apparently, the summation $$ \sum_{j = i + 1}^n \frac{1}{j - i + 1} $$ is equal to the summation $$ \sum_{k=1}^{n - i} \frac{1}{k + 1} $$ I don't grasp the intuition behind why.
David Faux
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How to prove that $\sum_{k=0}^{n} \frac{k-1}{k!} =\frac{-n-1}{(n+1)!}$

Just like in the question - how to prove that $\sum_{k=0}^{n} \frac{k-1}{k!} =\frac{-n-1}{(n+1)!}$ ? I will we thankful for any help.
Jerry
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Can we pull $f$ from this equation?

$$\sum_{k=1}^\infty f(k)\cdot e^{-k} = c$$ Can we pull $f$ function from this equation somehow? $c$ is a real constant...
esege
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Summation of$ n^3\over (3n)!$

Summation of $n^3\over(3n)!$ from 1 to infinity Please provide procedure. Don't know how to proceed. Tried making it to form $n^2\over3 (3n-1)!$ then?
user71408
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What is the infinite sum of regular numbers?

What and is the infinite sum of regular numbers? $\sum 1/r$ where r is regular number. Upto 10 digit accurate. Thanks Edit. http://oeis.org/A003592
Waqar Ahmad
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