List questions from binomial-theorem

Published on 23 Feb 2016 - 15:06

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Evaluate the following expression:

Published on 23 Feb 2016 - 17:00

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binomial expansion for non integer exponent $n$

Published on 24 Feb 2016 - 13:12

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Solve the following questions:

Published on 24 Feb 2016 - 14:01

322

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Minimum of $\sum\limits_{k=0}^n { n \choose k} (1-x)^{n-k} x^k a_{n-k}b_k$ over $x \in [0,1] $

Published on 24 Feb 2016 - 22:08

57

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Binomial expansion of $(x_{1}+x_{2}+...........+x_{k})^{n} $

Published on 24 Feb 2016 - 23:46

247

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Simplify $\binom nr+ 4\binom n{r+1} + 6\binom n{r+2} + 4\binom n{r+3}+\binom n{r+4}$

Published on 25 Feb 2016 - 8:21

161

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Using Newton Binomials and Combinatorics to reach this big O result?

Published on 25 Feb 2016 - 10:45

73

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Find the value of m for which the given sum is maximum:

Published on 25 Feb 2016 - 10:59

59

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Compute $\sum_{k=1}^{n+1} \binom{n}{k-2} \frac{2^k}{3^{2k-1}}$

Published on 26 Feb 2016 - 11:09

1.3k

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Expressing Factorials with Binomial Coefficients

Published on 26 Feb 2016 - 19:29

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N-th derivative of a product in binomial expansion?

Published on 26 Feb 2016 - 20:34

530

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Calculate chosen element of this Number Pyramid

Published on 27 Feb 2016 - 21:03

1.9k

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Let $X$ be a $B(n, 1/2)$ random variable with $n>=1$, show that the probability that $X$ is even is $1/2$.

Published on 01 Apr 2026 - 4:05

162

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Coefficient of $x^{n-1}$ in the given expansion

Published on 02 Mar 2016 - 20:17

List Question

Find the value of $a_r$ from the following equation

Evaluate the following expression:

binomial expansion for non integer exponent $n$

Solve the following questions:

Minimum of $\sum\limits_{k=0}^n { n \choose k} (1-x)^{n-k} x^k a_{n-k}b_k$ over $x \in [0,1] $

Binomial expansion of $(x_{1}+x_{2}+...........+x_{k})^{n} $

Simplify $\binom nr+ 4\binom n{r+1} + 6\binom n{r+2} + 4\binom n{r+3}+\binom n{r+4}$

Using Newton Binomials and Combinatorics to reach this big O result?

Find the value of m for which the given sum is maximum:

Compute $\sum_{k=1}^{n+1} \binom{n}{k-2} \frac{2^k}{3^{2k-1}}$

Expressing Factorials with Binomial Coefficients

N-th derivative of a product in binomial expansion?

Calculate chosen element of this Number Pyramid

Let $X$ be a $B(n, 1/2)$ random variable with $n>=1$, show that the probability that $X$ is even is $1/2$.

Coefficient of $x^{n-1}$ in the given expansion

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