List questions from binomial-theorem

Published on 28 Jan 2017 - 7:27

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What is the probability that exactly $2$ of them know Java?

Published on 02 Feb 2017 - 12:16

140

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Binomial Series Expansion

Published on 02 Feb 2017 - 17:15

360

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Binomial expansion and summation notation question

Published on 04 Feb 2017 - 16:43

77

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Asymptotic behaviour of $\binom{n+\alpha-1}{n}$

Published on 05 Feb 2017 - 1:50

331

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Combinatorial argument with the binomial theorem: $\binom{n}{0} + \binom{n}{1} 2 + \binom{n}{2} 2^2 + ... + \binom{n}{n} {2^n}$

Published on 27 Mar 2026 - 18:26

80

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Closed form for Binomial type of sum

Published on 08 Feb 2017 - 6:30

543

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Find the value of $\binom{2000}{2} + \binom{2000}{5} + \binom{2000}{8} + \cdots \binom{2000}{2000}$

Published on 09 Feb 2017 - 14:49

475

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Prove that $\sum_{k=0}^{n-r} \binom{r+k}{r} = \binom{n+1}{r+1}$

Published on 10 Feb 2017 - 3:26

163

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Closed form for $S= \sum\limits_{k=0}^n x^k \binom{n}{k}^2$

Published on 26 Mar 2026 - 4:31

709

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Divisibility problem (Based on binomial theorem)

Published on 11 Feb 2017 - 7:55

100

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How to expand a quadratic fraction using the binomial thereom

Published on 14 Feb 2017 - 13:52

228

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Find all positive integers $n$ such that $\displaystyle \left({-1 + i\sqrt{3}\over 2}\right)^n + \left({-1 - i\sqrt{3}\over 2}\right)^n = 2$?

Published on 15 Feb 2017 - 1:01

170

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Showing two series are equal to each other

Published on 16 Feb 2017 - 10:50

113

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Efficient evaluation of binomial series

Published on 16 Feb 2017 - 14:54

List Question

Show that $\sum_{k=0}^{n}(-1)^{n+k}{n\choose k}(ak+b)_n=n!a^n$

What is the probability that exactly $2$ of them know Java?

Binomial Series Expansion

Binomial expansion and summation notation question

Asymptotic behaviour of $\binom{n+\alpha-1}{n}$

Combinatorial argument with the binomial theorem: $\binom{n}{0} + \binom{n}{1} 2 + \binom{n}{2} 2^2 + ... + \binom{n}{n} {2^n}$

Closed form for Binomial type of sum

Find the value of $\binom{2000}{2} + \binom{2000}{5} + \binom{2000}{8} + \cdots \binom{2000}{2000}$

Prove that $\sum_{k=0}^{n-r} \binom{r+k}{r} = \binom{n+1}{r+1}$

Closed form for $S= \sum\limits_{k=0}^n x^k \binom{n}{k}^2$

Divisibility problem (Based on binomial theorem)

How to expand a quadratic fraction using the binomial thereom

Find all positive integers $n$ such that $\displaystyle \left({-1 + i\sqrt{3}\over 2}\right)^n + \left({-1 - i\sqrt{3}\over 2}\right)^n = 2$?

Showing two series are equal to each other

Efficient evaluation of binomial series

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