List questions from binomial-coefficients

Published on 26 Mar 2026 - 6:25

46

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Use of the Cartesian product and combinations

Published on 14 Apr 2026 - 17:43

242

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Is there a formula that gives the number of compositions of length $k$ of a number $n$ containing numbers no higher than $p$?

Published on 13 Apr 2026 - 17:28

110

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Newton's Binomial Theorem

Published on 13 Apr 2026 - 22:54

93

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Find $n$ if $\sum_{p=1}^{n}\sum_{q=p}^{n}(^nC_q)(^qC_p)=211$

Published on 17 Apr 2026 - 15:13

90

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Proving divisibility of a sum $\sum_{k=0}^{\lfloor{n/2}\rfloor} (-1)^{k}\binom{n}{2k} 7^{k}$

Published on 15 Apr 2026 - 5:37

119

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Prove: $\sum_{i=0}^{n-1} C_i\binom{2(n-i)-1}{n-i} = \binom{2n}{n+1}$

Published on 28 Mar 2026 - 10:24

100

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Central Binomial Coefficients and Multinomial Coefficients

Published on 26 Mar 2026 - 0:58

44

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Proving a binomial expansion inequality

Published on 14 Apr 2026 - 13:44

115

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Interpretation of $\sum^{n}_{k=0}\limits{\binom{n}{k}=2^{n}}$

Published on 11 Apr 2026 - 19:17

87

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proof for $\sum_{r=0}^{40} {40 \choose r} (-1)^r {100-r \choose 40} = 1$

Published on 14 Apr 2026 - 1:15

95

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Sum of factorials / binomial coefficients

Published on 11 Apr 2026 - 17:13

71

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Solve $\sin(n \arctan(\sqrt{15})) = \frac{\sqrt{15}}{2^{n+1}}$

Published on 16 Apr 2026 - 4:23

79

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Prove that $\sum\limits_{i=0}^n(-1)^i\binom{n}{i}\binom{kn-ki}{n-1}=0$

Published on 16 Apr 2026 - 2:45

74

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give a detailed proof of the following inequality for all integers n > 1

Published on 16 Apr 2026 - 12:28

List Question

Coefficient of $x^k$ in polynomial

Use of the Cartesian product and combinations

Is there a formula that gives the number of compositions of length $k$ of a number $n$ containing numbers no higher than $p$?

Newton's Binomial Theorem

Find $n$ if $\sum_{p=1}^{n}\sum_{q=p}^{n}(^nC_q)(^qC_p)=211$

Proving divisibility of a sum $\sum_{k=0}^{\lfloor{n/2}\rfloor} (-1)^{k}\binom{n}{2k} 7^{k}$

Prove: $\sum_{i=0}^{n-1} C_i\binom{2(n-i)-1}{n-i} = \binom{2n}{n+1}$

Central Binomial Coefficients and Multinomial Coefficients

Proving a binomial expansion inequality

Interpretation of $\sum^{n}_{k=0}\limits{\binom{n}{k}=2^{n}}$

proof for $\sum_{r=0}^{40} {40 \choose r} (-1)^r {100-r \choose 40} = 1$

Sum of factorials / binomial coefficients

Solve $\sin(n \arctan(\sqrt{15})) = \frac{\sqrt{15}}{2^{n+1}}$

Prove that $\sum\limits_{i=0}^n(-1)^i\binom{n}{i}\binom{kn-ki}{n-1}=0$

give a detailed proof of the following inequality for all integers n > 1

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