List questions from binomial-theorem

Published on 16 Mar 2014 - 15:49

108

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What is the coefficient of $x^{50}$ in $\left(x + \frac1x\right )^{100}$?

Published on 17 Mar 2014 - 14:45

114

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A combinatorics question on a sequence of binomial coefficents

Published on 19 Mar 2014 - 19:27

59

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Solve a product of binomials raised to a power for x

Published on 19 Mar 2014 - 19:54

138

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Prove $\sum\limits_{r=0}^{2n} r \binom{2n}{r}^2 = 2n \binom{4n-1}{2n}$

Published on 20 Mar 2014 - 9:08

73

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Prove $\binom{n+2}{k+2} = \binom{n}{k+2} + 2\binom{n}{k+1} + \binom{n}{k}$

Published on 20 Mar 2014 - 16:10

53

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show that these two equation holds by binomial theorem

Published on 25 Mar 2014 - 8:23

47

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How to get the series expansion?

Published on 26 Mar 2014 - 8:53

275

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The number of coin tosses needed if the proportion of heads is to lie within 0.05 of p with probability at least 0.9?

Published on 29 Mar 2014 - 2:09

53

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A question on multinomial theorem using binomial theorem

Published on 29 Mar 2014 - 13:58

68

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Sums, Binomial Coefficient

Published on 29 Mar 2014 - 23:11

341

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Meaning of double vertical bars in context: "let $q$ be a prime divisor of $n$ with $q^s|| n$."

Published on 26 Mar 2026 - 7:35

696

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Using the binomial expansion to solve a summation

Published on 30 Mar 2014 - 20:14

200

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Using the concept of the binomial expansion solve: $\sum_{k=0}^{n} \frac{1}{k+1} \binom{n}{k}$

Published on 30 Mar 2014 - 20:42

146

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Chu-Vandermonde-like combinatorial identity

Published on 31 Mar 2014 - 19:59

List Question

Finding divisibility of a

What is the coefficient of $x^{50}$ in $\left(x + \frac1x\right )^{100}$?

A combinatorics question on a sequence of binomial coefficents

Solve a product of binomials raised to a power for x

Prove $\sum\limits_{r=0}^{2n} r \binom{2n}{r}^2 = 2n \binom{4n-1}{2n}$

Prove $\binom{n+2}{k+2} = \binom{n}{k+2} + 2\binom{n}{k+1} + \binom{n}{k}$

show that these two equation holds by binomial theorem

How to get the series expansion?

The number of coin tosses needed if the proportion of heads is to lie within 0.05 of p with probability at least 0.9?

A question on multinomial theorem using binomial theorem

Sums, Binomial Coefficient

Meaning of double vertical bars in context: "let $q$ be a prime divisor of $n$ with $q^s|| n$."

Using the binomial expansion to solve a summation

Using the concept of the binomial expansion solve: $\sum_{k=0}^{n} \frac{1}{k+1} \binom{n}{k}$

Chu-Vandermonde-like combinatorial identity

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