Question

Prove the following combinatorial identity by differentiating the Binomial Theorem

score 188 · Answer 1 · 2020-10-01 21:04:56

188

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Prove the following combinatorial identity by differentiating the Binomial Theorem

Published on 01 Oct 2020 - 21:04

score 107 · Answer 2 · 2020-10-03 09:33:42

107

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Binomial coefficients prove $\sum_{k=0}^{n} {n+1\choose k+1}=2^{n+1}-1 $

Published on 03 Oct 2020 - 9:33

score 27 · Answer 3 · 2020-10-04 06:18:15

27

Views

Summation of special binomial series

Published on 04 Oct 2020 - 6:18

score 353 · Answer 4 · 2020-10-04 15:31:41

353

Views

Formula for sum of all binomial coefficients $\binom{n}{k}$ where $k$ is divisible by 4

Published on 04 Oct 2020 - 15:31

score 220 · Answer 5 · 2020-10-04 18:55:48

220

Views

Using Binomial Theorem to prove divisibility

Published on 04 Oct 2020 - 18:55

score 78 · Answer 6 · 2020-10-05 21:32:49

78

Views

Technique to calculate expectation/summation

Published on 05 Oct 2020 - 21:32

score 73 · Answer 7 · 2020-10-05 23:43:22

73

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Summation Simplification involving binomial coefficient

Published on 05 Oct 2020 - 23:43

score 121 · Answer 8 · 2020-10-06 21:59:02

121

Views

How to sum up $\binom{47} 4 \binom41 \binom{4-1}3 +\cdots+\binom{47}{47}\binom{47}1\binom{46}3$

Published on 06 Oct 2020 - 21:59

score 95 · Answer 9 · 2020-10-07 03:19:18

95

Views

Using the binomial theorem to prove for all integers $a$ and $b$, $a \big| \big((a + b)^n - b^n\big)$

Published on 07 Oct 2020 - 3:19

score 90 · Answer 10 · 2020-10-07 14:49:06

90

Views

Distribute 20 people into two queues with at least two

Published on 07 Oct 2020 - 14:49

score 94 · Answer 11 · 2020-10-08 07:53:52

94

Views

Prove $\frac{a^n−b^n}{a−b}=\sum _{k=0} ^{n−1} a^kb^{n−1−k}$ by Induction

Published on 08 Oct 2020 - 7:53

score 61 · Answer 12 · 2020-10-11 11:33:30

61

Views

The remainder left out when $8^{2n}-62^{2n+1}$ is divided by $9$ is?

Published on 11 Oct 2020 - 11:33

score 81 · Answer 13 · 2020-10-12 14:25:29

81

Views

Find the term independent of $x$ in the expansion below

Published on 12 Oct 2020 - 14:25

score 47 · Answer 14 · 2020-10-12 19:13:48

47

Views

Equivalent expression for $\sum_{m=0}^{n}{n \choose n-m}$

Published on 12 Oct 2020 - 19:13

score 91 · Answer 15 · 2020-10-14 15:13:46

91

Views

Find a closed formula (not including $\sum$) for the expression $\sum_{k=0}^{n-1}\binom{2n}{2k+1}$

Published on 14 Oct 2020 - 15:13

List Question

Prove the following combinatorial identity by differentiating the Binomial Theorem

Binomial coefficients prove $\sum_{k=0}^{n} {n+1\choose k+1}=2^{n+1}-1 $

Summation of special binomial series

Formula for sum of all binomial coefficients $\binom{n}{k}$ where $k$ is divisible by 4

Using Binomial Theorem to prove divisibility

Technique to calculate expectation/summation

Summation Simplification involving binomial coefficient

How to sum up $\binom{47} 4 \binom41 \binom{4-1}3 +\cdots+\binom{47}{47}\binom{47}1\binom{46}3$

Using the binomial theorem to prove for all integers $a$ and $b$, $a \big| \big((a + b)^n - b^n\big)$

Distribute 20 people into two queues with at least two

Prove $\frac{a^n−b^n}{a−b}=\sum _{k=0} ^{n−1} a^kb^{n−1−k}$ by Induction

The remainder left out when $8^{2n}-62^{2n+1}$ is divided by $9$ is?

Find the term independent of $x$ in the expansion below

Equivalent expression for $\sum_{m=0}^{n}{n \choose n-m}$

Find a closed formula (not including $\sum$) for the expression $\sum_{k=0}^{n-1}\binom{2n}{2k+1}$

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