Question

Prove that $\sum_{k=0}^{n}(-1)^k{n\choose k}\frac{1}{(k+1)(k+2)}=\frac{1}{n+2}$

score 186 · Answer 1 · 2026-04-14 16:25:51

186

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Prove that $\sum_{k=0}^{n}(-1)^k{n\choose k}\frac{1}{(k+1)(k+2)}=\frac{1}{n+2}$

Published on 14 Apr 2026 - 16:25

score 233 · Answer 2 · 2026-04-16 16:42:54

233

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Why are $\lfloor\zeta(\zeta(n))\rfloor$,$\left\lfloor\frac{1}{\zeta(n)-1}\right\rceil$, and $\lceil\Gamma(\zeta(n)-1)\rceil$ so similar?

Published on 16 Apr 2026 - 16:42

score 406 · Answer 3 · 2026-04-12 15:21:12

406

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Gamma fuction of odd numbers divided by 2

Published on 12 Apr 2026 - 15:21

score 94 · Answer 4 · 2026-04-15 21:30:04

94

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Why is $-\sqrt{\pi}$ not an answer to the Gaussian Integral?

Published on 15 Apr 2026 - 21:30

score 65 · Answer 5 · 2026-04-11 05:02:26

65

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How to evaluate this integral $\int_0^∞ ax^me^{-{ax}^n} dx$

Published on 11 Apr 2026 - 5:02

score 27 · Answer 6 · 2026-05-10 17:17:49

27

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Mistake in calculation $|c_l|^2\int_{0}^{2\pi}d\phi\int_{0}^{\pi}d\theta \sin(\theta)(\sin(\theta))^{2l}=1$

Published on 10 May 2026 - 17:17

score 67 · Answer 7 · 2026-04-11 00:23:26

67

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An evaluation about Gamma function

Published on 11 Apr 2026 - 0:23

score 125 · Answer 8 · 2026-04-11 23:11:42

125

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Approximation of $\Gamma(n+\lambda)/\Gamma(n)$ with $0<\lambda<1$ for large $n$

Published on 11 Apr 2026 - 23:11

score 403 · Answer 9 · 2026-05-10 15:26:43

403

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Gamma Function with Square

Published on 10 May 2026 - 15:26

score 208 · Answer 10 · 2026-04-09 10:54:04

208

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Explicit formula of Fourier Transform of $e^{-\pi x^4}$.

Published on 09 Apr 2026 - 10:54

score 279 · Answer 11 · 2026-04-20 17:05:04

279

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Telescoping sum involving $\int_0^\frac{\pi}{2}\cos^{2n} x\,dx$ and $\int_0^\frac{\pi}{2}x^2\cos^{2n} x\,dx$

Published on 17 Apr 2026 - 3:05

score 36 · Answer 13 · 2026-04-16 10:07:22

36

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What value of $k$ makes these relations equal? This is what I have tried...

Published on 16 Apr 2026 - 10:07

score 65 · Answer 14 · 2026-04-18 11:54:48

65

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closed form of series involving gamma function

Published on 18 Apr 2026 - 11:54

score 54 · Answer 15 · 2026-04-17 19:02:12

54

Views

Can $- (s^2 + (n + 1) s + n (n - 1)) \frac{\prod^{n - 2}_{^{} k = 1} (s - k)}{\prod^n_{k = 0} (s + k)}$ be written as a hypergeometric function?

Published on 17 Apr 2026 - 19:02

List Question

Prove that $\sum_{k=0}^{n}(-1)^k{n\choose k}\frac{1}{(k+1)(k+2)}=\frac{1}{n+2}$

Why are $\lfloor\zeta(\zeta(n))\rfloor$,$\left\lfloor\frac{1}{\zeta(n)-1}\right\rceil$, and $\lceil\Gamma(\zeta(n)-1)\rceil$ so similar?

Gamma fuction of odd numbers divided by 2

Why is $-\sqrt{\pi}$ not an answer to the Gaussian Integral?

How to evaluate this integral $\int_0^∞ ax^me^{-{ax}^n} dx$

Mistake in calculation $|c_l|^2\int_{0}^{2\pi}d\phi\int_{0}^{\pi}d\theta \sin(\theta)(\sin(\theta))^{2l}=1$

An evaluation about Gamma function

Approximation of $\Gamma(n+\lambda)/\Gamma(n)$ with $0<\lambda<1$ for large $n$

Gamma Function with Square

Explicit formula of Fourier Transform of $e^{-\pi x^4}$.

More elegant solution for showing that a distribution is unimodal

Telescoping sum involving $\int_0^\frac{\pi}{2}\cos^{2n} x\,dx$ and $\int_0^\frac{\pi}{2}x^2\cos^{2n} x\,dx$

What value of $k$ makes these relations equal? This is what I have tried...

closed form of series involving gamma function

Can $- (s^2 + (n + 1) s + n (n - 1)) \frac{\prod^{n - 2}_{^{} k = 1} (s - k)}{\prod^n_{k = 0} (s + k)}$ be written as a hypergeometric function?

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