Question

Can anyone help me to understand how this upper and lower bound for the binomial coefficient are derived?

score 115 · Answer 1 · 2020-05-25 09:24:29

115

Views

Can anyone help me to understand how this upper and lower bound for the binomial coefficient are derived?

Published on 25 May 2020 - 9:24

score 63 · Answer 2 · 2020-05-26 10:49:26

63

Views

Summation of binomial-like terms

Published on 26 May 2020 - 10:49

score 27 · Answer 3 · 2020-05-26 11:20:48

27

Views

Is there any way to generate solutions to a linear system given the domain of the terms (and some binomial products)?

Published on 26 May 2020 - 11:20

score 37 · Answer 4 · 2020-05-26 11:33:32

37

Views

Solving $C^{12}_{x} + C^{12}_{x+1} = C^{13}_{2x}$.

Published on 26 May 2020 - 11:33

score 363 · Answer 5 · 2026-03-25 17:20:11

363

Views

Prove: $\sum\limits_{k=0}^{n}\frac{1}{k+1}\binom{2k}{k}\binom{2n-2k}{n-k} = \binom{2n+1}{n}$

Published on 25 Mar 2026 - 17:20

score 128 · Answer 6 · 2026-03-30 13:03:16

128

Views

Evaluation of a tricky binomial sum

Published on 30 Mar 2026 - 13:03

score 171 · Answer 7 · 2026-03-29 12:52:06

171

Views

Reasoning about least common multiples and their relationship to binomial coefficients

Published on 29 Mar 2026 - 12:52

score 238 · Answer 8 · 2020-05-28 09:49:13

238

Views

Combinatorial problem: black and white balls divided into k groups with limits, and next picking a sequence of only black balls.

Published on 28 May 2020 - 9:49

score 119 · Answer 9 · 2020-05-28 10:41:58

119

Views

Combinatorial identity: $\sum_{i=0}^{k}\binom{n}{i}p^{i}q^{n-i}+ \sum_{i=k}^{n-1}\binom{i}{k}p^{k+1}q^{i-k}=1$.

Published on 28 May 2020 - 10:41

score 114 · Answer 10 · 2026-04-04 02:20:07

114

Views

Number of ordered Pairs satisfying $4^m-3^n=1$

Published on 04 Apr 2026 - 2:20

score 154 · Answer 11 · 2026-03-25 04:41:07

154

Views

Combinatorial identity: $\sum\limits_{k=0}^{i\land j}\binom ik(-1)^k\binom{i+j-k}i=1$

Published on 25 Mar 2026 - 4:41

score 215 · Answer 12 · 2026-03-25 09:50:03

215

Views

Calculating the number of poker hands that have exactly 4 different denominations

Published on 25 Mar 2026 - 9:50

score 82 · Answer 13 · 2020-05-29 08:37:18

82

Views

Solving $1+2+3+4+ \cdots+ n=$n(n+1)/2)$ $through use of binomial coefficient

Published on 29 May 2020 - 8:37

score 31 · Answer 14 · 2020-05-29 09:36:17

31

Views

How would I represent combinations of fixed subsets?

Published on 29 May 2020 - 9:36

score 131 · Answer 15 · 2020-05-29 17:56:53

131

Views

Represent $\sum_{k=1}^{n} k^{2}$ in terms of binomial coefficient.

Published on 29 May 2020 - 17:56

List Question

Can anyone help me to understand how this upper and lower bound for the binomial coefficient are derived?

Summation of binomial-like terms

Is there any way to generate solutions to a linear system given the domain of the terms (and some binomial products)?

Solving $C^{12}_{x} + C^{12}_{x+1} = C^{13}_{2x}$.

Prove: $\sum\limits_{k=0}^{n}\frac{1}{k+1}\binom{2k}{k}\binom{2n-2k}{n-k} = \binom{2n+1}{n}$

Evaluation of a tricky binomial sum

Reasoning about least common multiples and their relationship to binomial coefficients

Combinatorial problem: black and white balls divided into k groups with limits, and next picking a sequence of only black balls.

Combinatorial identity: $\sum_{i=0}^{k}\binom{n}{i}p^{i}q^{n-i}+ \sum_{i=k}^{n-1}\binom{i}{k}p^{k+1}q^{i-k}=1$.

Number of ordered Pairs satisfying $4^m-3^n=1$

Combinatorial identity: $\sum\limits_{k=0}^{i\land j}\binom ik(-1)^k\binom{i+j-k}i=1$

Calculating the number of poker hands that have exactly 4 different denominations

Solving $1+2+3+4+ \cdots+ n=$n(n+1)/2)$ $through use of binomial coefficient

How would I represent combinations of fixed subsets?

Represent $\sum_{k=1}^{n} k^{2}$ in terms of binomial coefficient.

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