Question

How to prove that $\sum_{k=1}^{\infty}\frac{k^{n+1}}{k!}=eB_{n+1}=1+\cfrac{2^n+\cfrac{3^n+\cfrac{4^n+\cfrac{\vdots}{4}}{3}}{2}}{1}$

score 206 · Answer 1 · 2018-12-21 23:18:13

206

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Published on 21 Dec 2018 - 23:18

score 83 · Answer 2 · 2018-12-22 07:10:55

83

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342

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667

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42

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score 337 · Answer 14 · 2019-02-14 01:59:08

337

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score 490 · Answer 15 · 2019-02-14 23:19:13

490

Views

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List Question

How to prove that $\sum_{k=1}^{\infty}\frac{k^{n+1}}{k!}=eB_{n+1}=1+\cfrac{2^n+\cfrac{3^n+\cfrac{4^n+\cfrac{\vdots}{4}}{3}}{2}}{1}$

Identifying the space of geodesics on the hyperbolic plane as a topological space.

Continued fraction of $\phi^3$

I have found a way of computing Euler's number. Is there any possible intuition of how that might be the case?

Simple continued fraction for irrational numbers.

Proof of this formula for $\sqrt{e\pi/2}$ and similar formulas.

Integral over recurrence relationship

Sequence Converging to the Square Root of an Integer $S \gt 1$

Non convergent simple continued fractions?

how to convert continued fractions into normal fractions?

Algorithm for regular continued fraction of a square root

The continued Fraction Algorithm Proofs

How to Compute Infinite Continued Factions

Let $x=1+\frac{1}{2+\frac{1}{1+\frac{1}{2+\frac{1}{...}}}}$; then the value of $(2x-1)^2$ equals...

Gauss measure and continued fraction

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