List questions from binomial-theorem

190

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Deriving $|\sum\limits_{k=0}^n (-1)^k \binom{n}{k}\binom{2n}{k}|\leq (\frac{16\sqrt 3}{9})^n $ where $|(z-1)^2(z+1)|\leq \frac{16\sqrt{3}}{9}$

Published on 24 Mar 2026 - 13:44

76

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Proving Binomial Equivalence

Published on 24 Mar 2026 - 5:14

581

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How to solve a binomial inequality

Published on 24 Mar 2026 - 14:50

98

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Sum Reduction (Binomial Theorem Related)

Published on 01 Apr 2018 - 17:18

354

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Can this be Combinatorial proof for $n2^{n-1}$ = $\sum_{k=0}^{n}k {n \choose k}$

Published on 02 Apr 2018 - 3:32

85

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Binomial Distribution where n = X?

Published on 25 Mar 2026 - 2:57

304

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Evaluate $\sum_{r=0}^{100} {(-1)^{r} {100 \choose r} {r^{50}}}$

Published on 24 Mar 2026 - 5:40

316

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Combinatorics - Choose Any Marble Exactly 4 times

Published on 02 Apr 2018 - 19:22

555

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Negative multinomial theorem?

Published on 23 Mar 2026 - 1:52

92

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An interesting extension of a combinatorics problem

Published on 23 Mar 2026 - 4:07

1.7k

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Find the last three digits of $19^{100}$

Published on 07 Apr 2018 - 10:12

1.1k

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Finding coefficient of $x^n$ in $(1-9x+20x^2)^{-1}$.

Published on 25 Mar 2026 - 0:52

58

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What is the expansion of $\sqrt{1+ux+vx^2}$ in powers of $x$?

Published on 20 Mar 2026 - 7:52

138

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Having trouble evaluating this integral using the binomial theorem.

Published on 25 Mar 2026 - 7:47

135

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Proving $\int_{0}^{2 \pi}\cos^{2n}(t)dt=2\pi\frac{1\cdot3\cdot5\cdots(2n-1)}{2\cdot4\cdot6\cdots(2n)}$

Published on 18 Apr 2018 - 14:26

List Question

Deriving $|\sum\limits_{k=0}^n (-1)^k \binom{n}{k}\binom{2n}{k}|\leq (\frac{16\sqrt 3}{9})^n $ where $|(z-1)^2(z+1)|\leq \frac{16\sqrt{3}}{9}$

Proving Binomial Equivalence

How to solve a binomial inequality

Sum Reduction (Binomial Theorem Related)

Can this be Combinatorial proof for $n2^{n-1}$ = $\sum_{k=0}^{n}k {n \choose k}$

Binomial Distribution where n = X?

Evaluate $\sum_{r=0}^{100} {(-1)^{r} {100 \choose r} {r^{50}}}$

Combinatorics - Choose Any Marble Exactly 4 times

Negative multinomial theorem?

An interesting extension of a combinatorics problem

Find the last three digits of $19^{100}$

Finding coefficient of $x^n$ in $(1-9x+20x^2)^{-1}$.

What is the expansion of $\sqrt{1+ux+vx^2}$ in powers of $x$?

Having trouble evaluating this integral using the binomial theorem.

Proving $\int_{0}^{2 \pi}\cos^{2n}(t)dt=2\pi\frac{1\cdot3\cdot5\cdots(2n-1)}{2\cdot4\cdot6\cdots(2n)}$

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