Question

Prove -1 Transformation (A binomial identity):$\binom{-p}{q}=\binom{p+q-1}{q}(-1)^q$

score 57 · Answer 1 · 2018-09-16 06:33:02

57

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Prove -1 Transformation (A binomial identity):$\binom{-p}{q}=\binom{p+q-1}{q}(-1)^q$

Published on 16 Sep 2018 - 6:33

score 105 · Answer 2 · 2018-09-17 22:39:04

105

Views

O level Expansion problem.

Published on 17 Sep 2018 - 22:39

score 1.9k · Answer 3 · 2018-09-29 09:11:14

1.9k

Views

Approximate $\sqrt{7}$ using binomial theorem

Published on 29 Sep 2018 - 9:11

score 99 · Answer 4 · 2026-03-26 01:26:25

99

Views

Characteristic Function and Generalized Binomial Theorem

Published on 26 Mar 2026 - 1:26

score 49 · Answer 5 · 2018-10-01 21:06:03

49

Views

Power Series / Taylor Expansion of $\frac{1}{\left(1-t^2\right)^{\frac{1}{2}}}$

Published on 01 Oct 2018 - 21:06

score 84 · Answer 6 · 2018-10-02 16:00:56

84

Views

Prove $3^{n−2} n (n − 1) = \sum_{k=2}^{n} \binom{n}{k} (k)(k − 1)2^{k−2}$ for $n\ge3$

Published on 02 Oct 2018 - 16:00

score 587 · Answer 7 · 2026-03-25 14:25:29

587

Views

Bacteria that doubles every time step with a probability of p or dies. What is expected number of bacteria after n time steps?

Published on 25 Mar 2026 - 14:25

score 1.6k · Answer 8 · 2018-10-04 08:58:28

1.6k

Views

Prove that $(x+y)^p=x^p+y^p \mod p$ where $p$ is a prime.

Published on 04 Oct 2018 - 8:58

score 1.4k · Answer 9 · 2018-10-06 17:29:19

1.4k

Views

How to prove divisibility of a number using the binomial expansion?

Published on 06 Oct 2018 - 17:29

score 3.7k · Answer 10 · 2018-10-06 17:43:33

3.7k

Views

prove that ${2n \choose n} \le 4^{n}$

Published on 06 Oct 2018 - 17:43

score 737 · Answer 11 · 2018-10-08 06:38:58

737

Views

Using the Binomial Theorem to expand the magnitude of the difference of two vectors

Published on 08 Oct 2018 - 6:38

score 3k · Answer 12 · 2018-10-10 03:03:37

3k

Views

Probability and Statistics: Over-booking flights

Published on 10 Oct 2018 - 3:03

score 192 · Answer 13 · 2026-03-25 14:19:56

192

Views

Rule of 72 binomial

Published on 25 Mar 2026 - 14:19

score 28 · Answer 14 · 2018-10-11 05:21:45

28

Views

Explanation In the orderings involving $2$ kinds of elements

Published on 11 Oct 2018 - 5:21

score 952 · Answer 15 · 2018-10-13 18:47:06

952

Views

Find the binomial expansion of the function up to the first 3 non-zero terms $\sqrt[3]\frac{1+2x}{1-x}$

Published on 13 Oct 2018 - 18:47

List Question

Prove -1 Transformation (A binomial identity):$\binom{-p}{q}=\binom{p+q-1}{q}(-1)^q$

O level Expansion problem.

Approximate $\sqrt{7}$ using binomial theorem

Characteristic Function and Generalized Binomial Theorem

Power Series / Taylor Expansion of $\frac{1}{\left(1-t^2\right)^{\frac{1}{2}}}$

Prove $3^{n−2} n (n − 1) = \sum_{k=2}^{n} \binom{n}{k} (k)(k − 1)2^{k−2}$ for $n\ge3$

Bacteria that doubles every time step with a probability of p or dies. What is expected number of bacteria after n time steps?

Prove that $(x+y)^p=x^p+y^p \mod p$ where $p$ is a prime.

How to prove divisibility of a number using the binomial expansion?

prove that ${2n \choose n} \le 4^{n}$

Using the Binomial Theorem to expand the magnitude of the difference of two vectors

Probability and Statistics: Over-booking flights

Rule of 72 binomial

Explanation In the orderings involving $2$ kinds of elements

Find the binomial expansion of the function up to the first 3 non-zero terms $\sqrt[3]\frac{1+2x}{1-x}$

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