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Proof that $\sum_{n=1}^{\infty}2^{-3n} = \frac{1}{7}$

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#summation #alternative-proof
385
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Multi-index sum property

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#combinatorics #summation
89
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Identity for $f(x) = \sum_{k=1}^{n}(x+k)^2$

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#summation
1.5k
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taking partial derivative of a sum

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#summation #partial-derivative
91
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Closed Form For Summation

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#combinatorics #summation #binomial-coefficients #exponentiation #closed-form
1.7k
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Is there a closed form for the sum of the reciprocal cubes of all coordinate distances?

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#summation #closed-form
236
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Recurrence equation from an infinite Fourier series

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#real-analysis #sequences-and-series #summation #fourier-analysis
97
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Is there any formula to compute $\sum_{k=1}^n\frac {1}{k^k}$?

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#sequences-and-series #algebra-precalculus #summation
189
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Prove $z^n + 1/{z^n}$ is rational if $z+1/z$ is rational

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#elementary-number-theory #summation #binomial-coefficients
191
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Is there any formula for $\sum_{k=1}^n k!$?

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#sequences-and-series #algebra-precalculus #summation
6.8k
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Asymptotics of $\sum\limits_{i=1}^n i\log i$

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#summation #logarithms #asymptotics #factorial
3.6k
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How to translate a Taylor Series into summation notation.

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#summation #taylor-expansion #summation-method
2.9k
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Prove that $\sum\limits_{j=k}^n\,(-1)^{j-k}\,\binom{j}{k}\,\binom{2n-j}{j}\,2^{2(n-j)}=\binom{2n+1}{2k+1}$.

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#combinatorics #complex-analysis #summation #binomial-coefficients #analytic-combinatorics
263
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Inverse of the sum $\sum\limits_{j=1}^k (-1)^{k-j}\binom{k}{j} j^{\,k} a_j$

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#analysis #summation #binomial-coefficients #analytic-combinatorics
205
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Find the Laurent Series expansion.

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#complex-analysis #summation #power-series #laurent-series

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