Question

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

score 184 · Answer 1 · 2026-03-25 05:50:17

184

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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 25 Mar 2026 - 5:50

score 230 · Answer 2 · 2018-05-01 06:27:46

230

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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 01 May 2018 - 6:27

score 403 · Answer 3 · 2018-05-01 22:24:49

403

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Gamma fuction of odd numbers divided by 2

Published on 01 May 2018 - 22:24

score 91 · Answer 4 · 2018-05-01 23:19:53

91

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

Published on 01 May 2018 - 23:19

score 62 · Answer 5 · 2018-05-02 11:14:01

62

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

Published on 02 May 2018 - 11:14

score 24 · Answer 6 · 2026-03-25 10:57:19

24

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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 25 Mar 2026 - 10:57

score 63 · Answer 7 · 2018-05-06 16:30:25

63

Views

An evaluation about Gamma function

Published on 06 May 2018 - 16:30

score 123 · Answer 8 · 2026-03-25 12:46:23

123

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

Published on 25 Mar 2026 - 12:46

score 400 · Answer 9 · 2026-03-25 12:21:28

400

Views

Gamma Function with Square

Published on 25 Mar 2026 - 12:21

score 206 · Answer 10 · 2018-05-11 15:42:35

206

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

Published on 11 May 2018 - 15:42

score 274 · Answer 11 · 2026-03-22 23:13:21

274

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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 13 May 2018 - 17:54

score 33 · Answer 13 · 2018-05-14 23:43:41

33

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

Published on 14 May 2018 - 23:43

score 61 · Answer 14 · 2026-03-25 08:07:53

61

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closed form of series involving gamma function

Published on 25 Mar 2026 - 8:07

score 51 · Answer 15 · 2018-05-19 15:06:20

51

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 19 May 2018 - 15:06

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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