Question

binomial congruence $\sum_{i=1}^{\frac{p-1}{2}}\binom{2i}{i}\equiv 0~or (-2)\pmod p$

score 619 · Answer 1 · 2016-11-09 08:33:31

619

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binomial congruence $\sum_{i=1}^{\frac{p-1}{2}}\binom{2i}{i}\equiv 0~or (-2)\pmod p$

Published on 09 Nov 2016 - 8:33

score 853 · Answer 2 · 2026-04-12 05:57:47

853

Views

Sum involving the product of binomial coefficients

Published on 12 Apr 2026 - 5:57

score 116 · Answer 3 · 2016-11-09 23:07:09

116

Views

Prove ${{n+1}\choose{m+1}} = \sum_{k=m}^{n}{k \choose m}$ by repeatedly using the Pascal Identity

Published on 09 Nov 2016 - 23:07

score 89 · Answer 4 · 2026-03-31 18:19:29

89

Views

Aproximation lg(n!)=n(lgn)-0.434)

Published on 31 Mar 2026 - 18:19

score 672 · Answer 5 · 2026-04-10 21:28:46

672

Views

Does a series of binomial coefficients converge?

Published on 10 Apr 2026 - 21:28

score 643 · Answer 6 · 2026-03-27 16:47:15

643

Views

Understanding the combinatorial argument for $\binom{\binom{n}{2}}{2} = 3 \binom{n+1}{4}$.

Published on 27 Mar 2026 - 16:47

score 471 · Answer 7 · 2016-11-10 17:54:30

471

Views

Binomial Coefficient of a Binomial Coefficient

Published on 10 Nov 2016 - 17:54

score 195 · Answer 8 · 2026-04-11 14:05:51

195

Views

Closed form for weighted sum involving product of binomial coefficients

Published on 11 Apr 2026 - 14:05

score 235 · Answer 9 · 2026-03-31 03:33:44

235

Views

Problem proving inequality $\frac{4^n}{n+1}\leq \frac{(2n)!}{(n!)^2}$

Published on 31 Mar 2026 - 3:33

score 64 · Answer 10 · 2016-11-11 14:40:58

64

Views

Prove that the expression $\frac{\gcd(n,m)}{n}\binom{n}{m}$ is an integer

Published on 11 Nov 2016 - 14:40

score 208 · Answer 11 · 2016-11-12 19:15:43

208

Views

Prove that $\binom{n}{1}+2\cdot\binom{n}{2}+3\cdot\binom{n}{3}+...+n\cdot\binom{n}{n}=n\cdot2^{n-1}$

Published on 12 Nov 2016 - 19:15

score 250 · Answer 12 · 2026-03-31 16:54:45

250

Views

By using calculus on $(1+x)^n$ and setting x equal to some appropriate number, evaluate:

Published on 31 Mar 2026 - 16:54

score 84 · Answer 13 · 2016-11-15 07:47:29

84

Views

Prove that $\sum_{k=1}^{n}(-1)^{k+1}\frac{1}{k}\binom{n}{k} = 1+\frac{1}{2} + \frac{1}{3} + ... + \frac{1}{n}$

Published on 15 Nov 2016 - 7:47

score 39 · Answer 14 · 2026-04-07 21:11:10

39

Views

how does the equation one solved in equation two

Published on 07 Apr 2026 - 21:11

score 878 · Answer 15 · 2026-04-12 18:44:15

878

Views

Proof Binomial Coefficient Identity: $\sum_{k=0}^n\frac{k k!}{n^k}\binom{n}{k}=n$

Published on 12 Apr 2026 - 18:44

List Question

binomial congruence $\sum_{i=1}^{\frac{p-1}{2}}\binom{2i}{i}\equiv 0~or (-2)\pmod p$

Sum involving the product of binomial coefficients

Prove ${{n+1}\choose{m+1}} = \sum_{k=m}^{n}{k \choose m}$ by repeatedly using the Pascal Identity

Aproximation lg(n!)=n(lgn)-0.434)

Does a series of binomial coefficients converge?

Understanding the combinatorial argument for $\binom{\binom{n}{2}}{2} = 3 \binom{n+1}{4}$.

Binomial Coefficient of a Binomial Coefficient

Closed form for weighted sum involving product of binomial coefficients

Problem proving inequality $\frac{4^n}{n+1}\leq \frac{(2n)!}{(n!)^2}$

Prove that the expression $\frac{\gcd(n,m)}{n}\binom{n}{m}$ is an integer

Prove that $\binom{n}{1}+2\cdot\binom{n}{2}+3\cdot\binom{n}{3}+...+n\cdot\binom{n}{n}=n\cdot2^{n-1}$

By using calculus on $(1+x)^n$ and setting x equal to some appropriate number, evaluate:

Prove that $\sum_{k=1}^{n}(-1)^{k+1}\frac{1}{k}\binom{n}{k} = 1+\frac{1}{2} + \frac{1}{3} + ... + \frac{1}{n}$

how does the equation one solved in equation two

Proof Binomial Coefficient Identity: $\sum_{k=0}^n\frac{k k!}{n^k}\binom{n}{k}=n$

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