List questions from binomial-theorem

Published on 03 Nov 2017 - 17:39

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Proving $\sum_{k=1}^n\binom{n}kk=n\,2^{n-1}$

Published on 05 Nov 2017 - 4:03

82

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Prove by induction $(1+x)^n > \frac {n(n-1)} 2 x^2$

Published on 08 Nov 2017 - 16:06

617

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Use complex numbers to find the summation of binomial coefficients of the following general form.

Published on 08 Nov 2017 - 18:40

62

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If the summation of $\frac{1}{^nC_r}$ is $a_n$, find the summation of $\frac{r}{^nC_r}$ in terms of $a_n$

Published on 11 Nov 2017 - 6:58

945

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Binomial-Theorem proof

Published on 12 Nov 2017 - 15:37

102

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High school probability question

Published on 02 Apr 2026 - 8:12

102

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From $(1+z)^p(1+z)^q=(1+z)^{p+q}$ show that $\sum\limits_{n=0}^r\binom{p}{n}\binom{q}{r-n}=\binom{p+q}{r}$ without using the Cauchy product

Published on 13 Nov 2017 - 15:46

390

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Prove that for all n $(-1)^1[nC1(1+rln10)/(1+ln10^n)^r1] +(-1)^2[nC2(1+rln10)/(1+ln10^n)^r]+....=0 $

Published on 15 Nov 2017 - 8:15

136

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Tricky question on binomial

Published on 23 Feb 2026 - 22:15

75

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similarity of the expansions of $e^x$ and $(1+x)^n$

Published on 16 Nov 2017 - 15:34

83

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help me in solving

Published on 19 Nov 2017 - 12:09

37

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Convergence range of Binomial Expansions with square unknowns?

Published on 19 Nov 2017 - 13:59

25.5k

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Coefficient of $x^{n-2}$ in $(x-1)(x-2)(x-3)\dotsm(x-n)$

Published on 19 Nov 2017 - 17:49

6.8k

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Sum of odd terms of a binomial expansion: $\sum\limits_{k \text{ odd}} {n\choose k} a^k b^{n-k}$

Published on 20 Nov 2017 - 10:30

List Question

Generalized binomial theorem for non-commuting matrices

Proving $\sum_{k=1}^n\binom{n}kk=n\,2^{n-1}$

Prove by induction $(1+x)^n > \frac {n(n-1)} 2 x^2$

Use complex numbers to find the summation of binomial coefficients of the following general form.

If the summation of $\frac{1}{^nC_r}$ is $a_n$, find the summation of $\frac{r}{^nC_r}$ in terms of $a_n$

Binomial-Theorem proof

High school probability question

From $(1+z)^p(1+z)^q=(1+z)^{p+q}$ show that $\sum\limits_{n=0}^r\binom{p}{n}\binom{q}{r-n}=\binom{p+q}{r}$ without using the Cauchy product

Prove that for all n $(-1)^1[nC1(1+rln10)/(1+ln10^n)^r1] +(-1)^2[nC2(1+rln10)/(1+ln10^n)^r]+....=0 $

Tricky question on binomial

similarity of the expansions of $e^x$ and $(1+x)^n$

help me in solving

Convergence range of Binomial Expansions with square unknowns?

Coefficient of $x^{n-2}$ in $(x-1)(x-2)(x-3)\dotsm(x-n)$

Sum of odd terms of a binomial expansion: $\sum\limits_{k \text{ odd}} {n\choose k} a^k b^{n-k}$

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