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Computing:$\sum_{n=0}^\infty\frac{3^n}{n!(n+3)}$

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#calculus #real-analysis #sequences-and-series #summation #power-series
493
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Prove that $1+{1\over 1+{1\over 1+{1\over 1+{1\over 1+...}}}}=\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+...}}}}$

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#sequences-and-series #limits #summation #contest-math #simple-functions
483
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Fourier series. Find the sum $\sum_{n=1}^\infty \frac{(-1)^{n+1}}{2n+1}$

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#summation #fourier-series
78
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Sigma (sum) Problem

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#calculus #summation
1.5k
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How to prove the inequality $\frac{1}{n}+\frac{1}{n+1}+\cdots+\frac{1}{2n-1}\geq \log (2)$?

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#inequality #summation #logarithms #problem-solving
312
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Double-exponential sum (maybe it telescopes?)

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#sequences-and-series #summation #generating-functions #telescopic-series
72
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Simplify $\prod_{k=1}^{l} \sum_{r=d}^m {{m}\choose{r}} \left(N-k \right)^{r} k^{m-r+1}$

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#sequences-and-series #summation #products
376
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Sum of two martingales

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#probability #summation #expectation #martingales
67
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How can we prove that $e^{-jωn}$ converges at $0$ while n -> infinity?

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#summation #fourier-transform
163
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Interesting inequalities

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#inequality #summation #radicals #fractions #a.m.-g.m.-inequality
167
Views

How to calculate the limit of a sum

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#calculus #summation
83
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Proving Combinatorics sum

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#combinatorics #summation
128
Views

How can I sum the series $e^{-2}\frac{(3)^n}{n!}\sum_{k=0}^{\infty}\left ( \frac{1}{2}\right )^k\frac{1}{(k-n)!}$

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#calculus #real-analysis #sequences-and-series #summation #closed-form
36
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Prove that $\forall\{x, y, z\}\subset\Bbb{Z}, \ \big(x+\frac{z}{2(x-y)}\big)^2-\big(y+\frac{z}{2(x-y)}\big)^2\in\Bbb{Z}$

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#proof-verification #summation
509
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Proof of (complicated?) summation equality

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#summation #combinatorial-proofs

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