Question

Binomial theorem and a congruence modulo $2^{2m+2}$

score 78 · Answer 1 · 2026-03-29 22:26:18

Binomial theorem and a congruence modulo $2^{2m+2}$

Published on 29 Mar 2026 - 22:26

score 52 · Answer 2 · 2021-01-19 18:26:21

The value of $r$ for which $\binom {20}{r} \binom{20}{0} +\binom{20}{r-1}\binom{20}{1}...\binom{20}{0} \binom{20}{r}$ is maximum is?

score 153 · Answer 3 · 2021-01-21 00:27:09

153

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Evaluating $\sum\limits_{i=0}^n{n\choose i}2^i$

Published on 21 Jan 2021 - 0:27

score 60 · Answer 4 · 2021-01-23 10:31:25

60

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How $\sum\limits_{k=0}^n {n\choose k}\cdot 0^{n-k}\cdot 2^{k}=2^{n}$?

Published on 23 Jan 2021 - 10:31

score 122 · Answer 5 · 2026-03-30 12:22:34

122

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Evaluating $\sum_{i=0}^{30}(-1)^i {{30} \choose {i}}(30-i)^{31}$

Published on 30 Mar 2026 - 12:22

score 40 · Answer 6 · 2021-01-30 05:54:33

40

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Rewriting a Binomial expansion and expanding the rewritten version after making a convenience substitution to get a totally different answer

Published on 30 Jan 2021 - 5:54

score 82 · Answer 7 · 2021-01-30 13:26:24

82

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Let $X$ be a set of $5$ elements. Find the number of ordered pairs $(A,B)$ of subsets of $X$ such that $A, B\neq \emptyset$ and $A\cap B=\emptyset$

Published on 30 Jan 2021 - 13:26

score 386 · Answer 8 · 2021-01-31 16:16:40

386

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Upper bound for - $\sum_{i=1}^n i {2n \choose n+i} $.

Published on 31 Jan 2021 - 16:16

score 47 · Answer 9 · 2021-02-01 15:45:59

47

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Find $n$ such that the $10th$ term of the binomial expansion $(5+n)^n$ to be the greatest term.

Published on 01 Feb 2021 - 15:45

score 652 · Answer 10 · 2021-02-01 22:30:31

652

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Intuitive explanation for negative binomial expansion

Published on 01 Feb 2021 - 22:30

score 142 · Answer 11 · 2021-02-02 11:16:54

142

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Binomial Theorem Inequality

Published on 02 Feb 2021 - 11:16

score 100 · Answer 12 · 2021-02-03 04:34:11

100

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Show $\sum_{k=0}^{n} \binom{x}{k} \binom{y}{n-k} = \binom{x+y}{n}$.

Published on 03 Feb 2021 - 4:34

score 144 · Answer 13 · 2021-02-03 06:35:08

144

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Show $\sum_{k=0}^{n} \binom{2k}{k} \binom{2(n-k)}{n-k} = 4^n$.

Published on 03 Feb 2021 - 6:35

score 38 · Answer 14 · 2021-02-03 21:44:41

38

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How to find the coefficient of $x^2y^3z^6$ in the expression $(x+y+xz)^{4}(y+z)^3$?

Published on 03 Feb 2021 - 21:44

score 27 · Answer 15 · 2026-03-29 11:07:03

27

Views

Expansion of $b^{(x+a)^{-n}}$ where $0 \le b \le 1$

Published on 29 Mar 2026 - 11:07

List Question

Binomial theorem and a congruence modulo $2^{2m+2}$

The value of $r$ for which $\binom {20}{r} \binom{20}{0} +\binom{20}{r-1}\binom{20}{1}...\binom{20}{0} \binom{20}{r}$ is maximum is?

Evaluating $\sum\limits_{i=0}^n{n\choose i}2^i$

How $\sum\limits_{k=0}^n {n\choose k}\cdot 0^{n-k}\cdot 2^{k}=2^{n}$?

Evaluating $\sum_{i=0}^{30}(-1)^i {{30} \choose {i}}(30-i)^{31}$

Rewriting a Binomial expansion and expanding the rewritten version after making a convenience substitution to get a totally different answer

Let $X$ be a set of $5$ elements. Find the number of ordered pairs $(A,B)$ of subsets of $X$ such that $A, B\neq \emptyset$ and $A\cap B=\emptyset$

Upper bound for - $\sum_{i=1}^n i {2n \choose n+i} $.

Find $n$ such that the $10th$ term of the binomial expansion $(5+n)^n$ to be the greatest term.

Intuitive explanation for negative binomial expansion

Binomial Theorem Inequality

Show $\sum_{k=0}^{n} \binom{x}{k} \binom{y}{n-k} = \binom{x+y}{n}$.

Show $\sum_{k=0}^{n} \binom{2k}{k} \binom{2(n-k)}{n-k} = 4^n$.

How to find the coefficient of $x^2y^3z^6$ in the expression $(x+y+xz)^{4}(y+z)^3$?

Expansion of $b^{(x+a)^{-n}}$ where $0 \le b \le 1$

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