Question

Two Euler type sums involving binomial coefficient and harmonic number

score 151 · Answer 1 · 2026-03-25 17:29:50

151

Views

Two Euler type sums involving binomial coefficient and harmonic number

Published on 25 Mar 2026 - 17:29

score 595 · Answer 2 · 2019-06-05 08:06:32

595

Views

Proving that $\sum_{k=0}^{n}\frac{(-1)^k}{{n\choose k}}=[1+(-1)^n] \frac{n+1}{n+2}.$

Published on 05 Jun 2019 - 8:06

score 55 · Answer 3 · 2019-06-06 11:44:08

55

Views

Proof $C_h = \binom{2^h-2}{2^{h-1}-1} C_{h-1}^2$ can be written non-recursively as $C_h = \frac{(2^h-1)!}{\prod_{k=1}^h (2^k-1)^{2^{h-k}}}. $

Published on 06 Jun 2019 - 11:44

score 113 · Answer 4 · 2026-03-26 01:28:40

113

Views

Proof needed for the combinatorial identity $\sum_{a=0}^n\binom{n+a}{a}/{2^{n+a}}=1$

Published on 26 Mar 2026 - 1:28

score 502 · Answer 5 · 2026-03-27 03:48:15

502

Views

Sum of reciprocal binomial coefficients

Published on 27 Mar 2026 - 3:48

score 370 · Answer 6 · 2026-03-25 11:00:58

370

Views

A bug in Wolfram Alpha about an infinite series?

Published on 25 Mar 2026 - 11:00

score 48 · Answer 7 · 2026-03-26 04:34:54

48

Views

Show $\frac1{(n(n+1))^m} =\sum_{k=0}^{m-1} a_{m,k}(-1)^k(\frac1{n^{m-k}}+(-1)^{m-k}\frac1{(n+1)^{m-k}}) $ where $a_{m, k} =\binom{ m-1+k}{k} $

Published on 26 Mar 2026 - 4:34

score 290 · Answer 8 · 2026-03-25 01:20:25

290

Views

Is there an identity between the Clausen function $\rm{Cl}_8\left(\frac\pi3\right)$ and $\sum_{n=1}^\infty \frac{1}{n^9\,\binom {2n}n}$?

Published on 25 Mar 2026 - 1:20

score 119 · Answer 9 · 2019-06-11 05:26:59

119

Views

Calculate the limit including binomial coefficients

Published on 11 Jun 2019 - 5:26

score 40 · Answer 10 · 2019-06-11 13:56:03

40

Views

Solving binomial expansions given some information about the coefficients of x.

Published on 11 Jun 2019 - 13:56

score 56 · Answer 11 · 2019-06-11 23:29:12

56

Views

Finding the coefficient of $x^n $ in a rational expression

Published on 11 Jun 2019 - 23:29

score 77 · Answer 12 · 2019-06-12 04:10:33

77

Views

Prove that $\sum_{j = 0}^p {p \choose j}{p + j \choose j} \equiv 2^p + 1 ~(\text{mod}~p^2)$

Published on 12 Jun 2019 - 4:10

score 97 · Answer 13 · 2019-06-12 20:37:54

97

Views

Finding proof of sum of products of binomial coefficients.

Published on 12 Jun 2019 - 20:37

score 138 · Answer 14 · 2019-06-12 22:27:05

138

Views

Alternately Multiplying and Dividing Within Pascal's Triangle

Published on 12 Jun 2019 - 22:27

score 130 · Answer 15 · 2019-06-13 11:06:56

130

Views

How to find sum $\sum_{x=1}^K x^n(x-1)^m$

Published on 13 Jun 2019 - 11:06

List Question

Two Euler type sums involving binomial coefficient and harmonic number

Proving that $\sum_{k=0}^{n}\frac{(-1)^k}{{n\choose k}}=[1+(-1)^n] \frac{n+1}{n+2}.$

Proof $C_h = \binom{2^h-2}{2^{h-1}-1} C_{h-1}^2$ can be written non-recursively as $C_h = \frac{(2^h-1)!}{\prod_{k=1}^h (2^k-1)^{2^{h-k}}}. $

Proof needed for the combinatorial identity $\sum_{a=0}^n\binom{n+a}{a}/{2^{n+a}}=1$

Sum of reciprocal binomial coefficients

A bug in Wolfram Alpha about an infinite series?

Show $\frac1{(n(n+1))^m} =\sum_{k=0}^{m-1} a_{m,k}(-1)^k(\frac1{n^{m-k}}+(-1)^{m-k}\frac1{(n+1)^{m-k}}) $ where $a_{m, k} =\binom{ m-1+k}{k} $

Is there an identity between the Clausen function $\rm{Cl}_8\left(\frac\pi3\right)$ and $\sum_{n=1}^\infty \frac{1}{n^9\,\binom {2n}n}$?

Calculate the limit including binomial coefficients

Solving binomial expansions given some information about the coefficients of x.

Finding the coefficient of $x^n $ in a rational expression

Prove that $\sum_{j = 0}^p {p \choose j}{p + j \choose j} \equiv 2^p + 1 ~(\text{mod}~p^2)$

Finding proof of sum of products of binomial coefficients.

Alternately Multiplying and Dividing Within Pascal's Triangle

How to find sum $\sum_{x=1}^K x^n(x-1)^m$

Trending Questions

Popular # Hahtags

Popular Questions