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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What methods can I use to solve this equation?

I solved it by just trying out various x's, but is there a better way to solve this and how is this 'brute force' way of solving called? I am sorry, I don't know the terminology exactly.
brikas
  • 111
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Is there a formula for this specific summation

The summation goes as follows: 0 + 1 + 3 + 6 + 10 + 15 ... and $k $ starts at 1 where k is the current iteration and where the next number is equal to the previous number plus the previous iteration $k$.
KetDog
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Simplify Double Summation with interdependencies

I'm trying to understand the worst-case time complexity of the kth permutation coding problem. That is, how do I simplify the following: $$ \sum_{l=1}^{n} \sum_{i=0}^{n-l} 2l+m $$ to $$ \frac{1}{6}n(n+1)(3m+2n+4) $$
Mike
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Is there a summation that can add on top of itself up to m times?

I do think I'm wording this somewhat incorrect so I'll do my best to explain what my goal is. I'm trying to create a summation that adds $n$ values repeatedly until $m$. So it'd look something like this: $(0) + (0+1)+ (0+1+2) + ... +…
Nom
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Generalizing a series of summations

I have $E(x)$, where $x$ goes from $0$ to $A$. For the sake of brevity, let $0 = E(0)$, $1 = E(1)$, $2 = E(2)$, etc... I want to sum the combinations of these to a depth of $B$, such that if $A=2$ I get: $B = 1: 0 + 1 + 2$ $B = 2: 00 + 01 + 02 + 11…
Laukei
  • 11
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Einstein Summation involving Exponents

According to a version of Einstein summation convention, an expression with a repeated dummy index that appears as both a prefix and a suffix is understood to be a summation over that index. Under this convention, the prefix is not an exponent. To…
Ka Fat Chow
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Complicated summation involving Lerch Transcendent.

I would like to solve a long summation related to mean residual life for a new discrete distribution but I have difficulty to solve the following summation (a part of larger summation), which is given as $$ \sum_{j=x}^{\infty} p^j…
RRMT
  • 101
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Function asymptotic to quotient of summations

Given the function $Q$ that takes as input two sequences of positive integers $X = [x_1, x_2, ... x_n]$ and $Y = [y_1, y_2, ... y_n]$, $n \in [1, ... \infty]$ and returns the quotient of their sums $$ Q(X, Y) = \frac{\sum_{i=0}^n x_i}{\sum_{i=0}^n…
Federico Taschin
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divergence of $ \sum_{n=1}^{\infty}\arcsin(1/n)$

$ \sum_{n=1}^{\infty}\arcsin(1/n)$ need some hint to prove that this sum is DIVERGENT i have tried wolfram alpha and the partial series seems to go increasing so $ S(k)
Jose Garcia
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What is the average area of the squares in a $15000$m dotted grid where each dot is $1$m away

What is the average area of the squares in a 15000m dotted grid where each dot is 1m away I've been struggling with this question because of two things : First, I can't think of a way to calculate the area of oblique squares (although I can count…
David G.
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Sum of a geometric progression

Just a very small query, I am currently looking at the solutions to a question, and the final step is: $c$ $\sum_{k=1}^\infty p^k$ = $\frac{cp}{1-p}$ Is this correct? I thought this formula only held when it went from k = 0 to infinity?
user1062310
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Some further explanation on a summation

I am having a bit of trouble with this passage in the summation, could you guys help understand what's happening? $$\frac{1}{4}\sum_{i\leq{n}}({\frac{2}{3}})^n=\frac{3}{4}(\frac{2}{3})^i$$ Is it a purely algebraic passage or is it something more…
Ramiro genta
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Summation Series for fractions

I have a summation series of the form: $n + n/2 + n/4 + n/8 + n/16 +\ldots + 1$. Is there a formula for this series? Basically, the denominators are powers of 2.
John Doe
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Where can I find more information about this equation

Is this equation special somehow? $$ \frac{\sum{xy}}{\sum{x}} $$ Can this be simplified or written alternately? Or is this its most basic form already? Sorry for not using the right mathematical terms here... mainly wondering if I should try to…
Veldaeven
  • 109
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Double summation - How to solve for $\sum_{j=i}^n 1?$

Could someone please help understand how this can be simplified? I don't understand how to solve/isolate the rightmost summation. $$\sum_{i=1}^n \sum_{j=i}^n 1$$
1nternetz
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