List questions from binomial-theorem

Published on 25 Mar 2026 - 17:38

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What happens from $ (1+(x+x^2))^n$ to $\sum_k {n \choose k} (x+x^2)^n$?

Published on 21 Dec 2014 - 6:37

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If $k, m, n$, are natural numbers and $k \leq n$ What is the final answer of this :

Published on 21 Dec 2014 - 16:10

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Combinatoric proof for $\sum_{k=0}^n{n\choose k}\left(-1\right)^k\left(n-k\right)^4 = 0$ ($n\geqslant5$)

Published on 26 Mar 2026 - 11:18

106

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Sum of binomial coefficients $\sum _{ x=r-2 }^{ n-2 } \binom{x}{r-2}$

Published on 26 Dec 2014 - 19:05

86

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$(1+x)^n \ge \frac{n(n-1)}{2}x^2$ is there something wrong in my proof?

Published on 26 Dec 2014 - 23:25

82

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Prove that $(1-t^6)^6 = \sum_{j=0}^{6} {6 \choose j} (-1)^jt^{6j} $ using the binomial theorem

Published on 28 Dec 2014 - 22:57

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How to prove $\sum_{k=1}^{n}k\binom{n}{k} = n2^{n-1}$

Published on 29 Dec 2014 - 8:10

111

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Elementary "binomial theorem" in English

Published on 02 Jan 2015 - 14:31

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The status of the sum: $\sum_{k=m}^{n} \frac{{k \choose m}}{k+1}$

Published on 02 Oct 2019 - 13:21

40

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Confusion about binomial theorem

Published on 03 Oct 2019 - 11:56

69

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What is the sum of the given series?

Published on 03 Oct 2019 - 18:17

1.9k

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How to find number of distinct terms in a multinomial expansion?

Published on 04 Oct 2019 - 8:31

16

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Relation between number of possible arrangements of $x's$ and $y's$ and the coefficient of the $(r+1)^{th}$ term

Published on 11 Mar 2026 - 0:10

105

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Difference between binomial expansions

Published on 05 Oct 2019 - 18:53

List Question

Finding number of integral solutions

What happens from $ (1+(x+x^2))^n$ to $\sum_k {n \choose k} (x+x^2)^n$?

If $k, m, n$, are natural numbers and $k \leq n$ What is the final answer of this :

Combinatoric proof for $\sum_{k=0}^n{n\choose k}\left(-1\right)^k\left(n-k\right)^4 = 0$ ($n\geqslant5$)

Sum of binomial coefficients $\sum _{ x=r-2 }^{ n-2 } \binom{x}{r-2}$

$(1+x)^n \ge \frac{n(n-1)}{2}x^2$ is there something wrong in my proof?

Prove that $(1-t^6)^6 = \sum_{j=0}^{6} {6 \choose j} (-1)^jt^{6j} $ using the binomial theorem

How to prove $\sum_{k=1}^{n}k\binom{n}{k} = n2^{n-1}$

Elementary "binomial theorem" in English

The status of the sum: $\sum_{k=m}^{n} \frac{{k \choose m}}{k+1}$

Confusion about binomial theorem

What is the sum of the given series?

How to find number of distinct terms in a multinomial expansion?

Relation between number of possible arrangements of $x's$ and $y's$ and the coefficient of the $(r+1)^{th}$ term

Difference between binomial expansions

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