Question

Combinatorial Argument for a Binomial idenity

score 137 · Answer 1 · 2026-04-13 06:40:02

137

Views

Combinatorial Argument for a Binomial idenity

Published on 13 Apr 2026 - 6:40

score 36 · Answer 2 · 2026-04-16 13:18:37

36

Views

Closed form for the number of $\mathbf{q} \in \Bbb{Z}^n$ with $\|\mathbf{q}\|_{\infty} = h$

Published on 16 Apr 2026 - 13:18

score 39 · Answer 3 · 2026-04-13 01:07:36

39

Views

Field of convergence, prove it's open?

Published on 13 Apr 2026 - 1:07

score 208 · Answer 4 · 2026-05-11 04:10:46

208

Views

Sum of Squares for $a^2+b^2+c^2+d^2+abcd+1\ge ab+bc+cd+da + ac+bd$

Published on 11 May 2026 - 4:10

score 44 · Answer 5 · 2026-04-13 09:26:09

44

Views

Sum of elements in two different subsets of a set

Published on 13 Apr 2026 - 9:26

score 71 · Answer 6 · 2026-04-12 01:21:47

71

Views

Sum $\lim_{x\to -\infty} \sum_{k=1}^{1000} \frac{x^k}{k!}$

Published on 12 Apr 2026 - 1:21

score 819 · Answer 7 · 2026-04-17 02:48:30

819

Views

Proving $ \sum _{k=0} ^m \binom nk \binom{n-k}{m-k} = 2^m \binom {n}{m}$.

Published on 17 Apr 2026 - 2:48

score 306 · Answer 8 · 2026-04-12 14:09:53

306

Views

Identity for sum of binomial coefficients derived from convolution of negative binomial random variables

Published on 12 Apr 2026 - 14:09

score 138 · Answer 9 · 2026-05-11 05:30:47

138

Views

Proving $\frac{1}{16} \sum \frac{(b+c)(c+a)}{ab} +\frac{9}{4} \geq 4\sum \frac{ab}{(b+c)(c+a)}$

Published on 11 May 2026 - 5:30

score 50 · Answer 10 · 2026-04-14 08:08:44

50

Views

Proving That $\sum^{n}_{k=0} \bigl(\frac{4}{5}\bigr)^k < 5$

Published on 14 Apr 2026 - 8:08

score 85 · Answer 11 · 2026-04-16 09:56:24

85

Views

Prove combinatorically, that for $n \geq m$: $\sum_{k=0}^m \dbinom{n}{k} \dbinom{n-k}{m-k}= 2^m \dbinom{n}{m}$

Published on 16 Apr 2026 - 9:56

score 52 · Answer 12 · 2026-04-17 13:54:42

52

Views

Show that $F(x)=\frac{x}{(1-x)^2}-\frac{2x}{(2-x)^2}=\sum_{n=0}^{\infty}n(1-2^{-n})x^n$

Published on 17 Apr 2026 - 13:54

score 48 · Answer 13 · 2026-04-12 19:10:51

48

Views

The "calculus" of sums, i.e. $\sum_{j=0}^{2k}-\sum_{j=0}^k$

Published on 12 Apr 2026 - 19:10

score 236 · Answer 14 · 2026-04-16 10:08:19

236

Views

Question about product of generating functions in a proof that for positive integer $n$, $\sum_{k=0}^n(-1)^k\binom nk\binom{2n-k}n=1$.

Published on 16 Apr 2026 - 10:08

score 103 · Answer 15 · 2026-04-16 02:40:50

103

Views

The summation $\sum_{n\geqslant1} \frac1n\sum_{d\mid n}\frac{d}{n^2+d}.$

Published on 16 Apr 2026 - 2:40

List Question

Combinatorial Argument for a Binomial idenity

Closed form for the number of $\mathbf{q} \in \Bbb{Z}^n$ with $\|\mathbf{q}\|_{\infty} = h$

Field of convergence, prove it's open?

Sum of Squares for $a^2+b^2+c^2+d^2+abcd+1\ge ab+bc+cd+da + ac+bd$

Sum of elements in two different subsets of a set

Sum $\lim_{x\to -\infty} \sum_{k=1}^{1000} \frac{x^k}{k!}$

Proving $ \sum _{k=0} ^m \binom nk \binom{n-k}{m-k} = 2^m \binom {n}{m}$.

Identity for sum of binomial coefficients derived from convolution of negative binomial random variables

Proving $\frac{1}{16} \sum \frac{(b+c)(c+a)}{ab} +\frac{9}{4} \geq 4\sum \frac{ab}{(b+c)(c+a)}$

Proving That $\sum^{n}_{k=0} \bigl(\frac{4}{5}\bigr)^k < 5$

Prove combinatorically, that for $n \geq m$: $\sum_{k=0}^m \dbinom{n}{k} \dbinom{n-k}{m-k}= 2^m \dbinom{n}{m}$

Show that $F(x)=\frac{x}{(1-x)^2}-\frac{2x}{(2-x)^2}=\sum_{n=0}^{\infty}n(1-2^{-n})x^n$

The "calculus" of sums, i.e. $\sum_{j=0}^{2k}-\sum_{j=0}^k$

Question about product of generating functions in a proof that for positive integer $n$, $\sum_{k=0}^n(-1)^k\binom nk\binom{2n-k}n=1$.

The summation $\sum_{n\geqslant1} \frac1n\sum_{d\mid n}\frac{d}{n^2+d}.$

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