Question

Equating coefficients of binomial expansion modulo p

score 736 · Answer 1 · 2015-11-20 11:33:19

736

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Equating coefficients of binomial expansion modulo p

Published on 20 Nov 2015 - 11:33

score 194 · Answer 2 · 2015-11-20 13:38:33

194

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Using generating functions show that $\sum^n _{r=1}r\binom{n}{r}\binom{m}{r} =n\binom{n+m-1}{n}$

Published on 20 Nov 2015 - 13:38

score 463 · Answer 3 · 2015-11-21 12:53:18

463

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Prove identity $1 + {n \choose 3} + {n \choose 6} + \cdots = \frac{1}{3}\left(2^n + 2\cos{\frac{n\pi}{3}}\right)$ without using complex numbers

Published on 21 Nov 2015 - 12:53

score 128 · Answer 4 · 2015-11-22 19:44:34

128

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Binomial Theorem twice in one equation?

Published on 22 Nov 2015 - 19:44

score 254 · Answer 5 · 2015-11-25 14:49:52

254

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Binomial theorem and the inequality $(1-e^{-x})^{\alpha}\leq (1-\alpha e^{-x})$ for $0<\alpha\le 1$

Published on 25 Nov 2015 - 14:49

score 122 · Answer 6 · 2015-11-25 17:30:55

122

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Finding the values for satisfying the given equality $x+y+z=7$

Published on 25 Nov 2015 - 17:30

score 55 · Answer 7 · 2015-11-25 19:42:59

55

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Fibonacci numbers and binomial theroem

Published on 25 Nov 2015 - 19:42

score 134 · Answer 8 · 2015-11-25 22:42:19

134

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Binomial Theorem proof using Cauchy Induction

Published on 25 Nov 2015 - 22:42

score 309 · Answer 9 · 2015-11-26 17:14:17

309

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Finding $\binom n0+\binom n3+\binom n6+\cdots $

Published on 26 Nov 2015 - 17:14

score 98 · Answer 10 · 2015-11-26 17:20:00

98

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Evaluate: $\sum\limits_{k=0}^{n}k^2{n\choose k}(\frac{1}{3})^k(\frac{2}{3})^{n-k}$

Published on 26 Nov 2015 - 17:20

score 3.3k · Answer 11 · 2026-03-28 16:14:04

3.3k

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Prove $\sum_{i=0}^n {{n \choose i} \times 2^i} = 3^n $

Published on 28 Mar 2026 - 16:14

score 101 · Answer 12 · 2015-11-29 19:03:43

101

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Prove E(x)=pn by taking derivative of Newtons binomial theroem

Published on 29 Nov 2015 - 19:03

score 285 · Answer 13 · 2026-04-01 18:34:06

285

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What is $\lfloor(\sqrt 3 +1)^5\rfloor$? (without a calculator)

Published on 01 Apr 2026 - 18:34

score 55 · Answer 14 · 2015-11-30 17:25:04

55

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What is coefficient of $x^k$ in $ n! (x/1! + x^2/2! + x^3/3! + ... )^n$?

Published on 30 Nov 2015 - 17:25

score 96 · Answer 15 · 2015-12-03 01:16:48

96

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discrete math binomial theorem problem: computing the sum

Published on 03 Dec 2015 - 1:16

List Question

Equating coefficients of binomial expansion modulo p

Using generating functions show that $\sum^n _{r=1}r\binom{n}{r}\binom{m}{r} =n\binom{n+m-1}{n}$

Prove identity $1 + {n \choose 3} + {n \choose 6} + \cdots = \frac{1}{3}\left(2^n + 2\cos{\frac{n\pi}{3}}\right)$ without using complex numbers

Binomial Theorem twice in one equation?

Binomial theorem and the inequality $(1-e^{-x})^{\alpha}\leq (1-\alpha e^{-x})$ for $0<\alpha\le 1$

Finding the values for satisfying the given equality $x+y+z=7$

Fibonacci numbers and binomial theroem

Binomial Theorem proof using Cauchy Induction

Finding $\binom n0+\binom n3+\binom n6+\cdots $

Evaluate: $\sum\limits_{k=0}^{n}k^2{n\choose k}(\frac{1}{3})^k(\frac{2}{3})^{n-k}$

Prove $\sum_{i=0}^n {{n \choose i} \times 2^i} = 3^n $

Prove E(x)=pn by taking derivative of Newtons binomial theroem

What is $\lfloor(\sqrt 3 +1)^5\rfloor$? (without a calculator)

What is coefficient of $x^k$ in $ n! (x/1! + x^2/2! + x^3/3! + ... )^n$?

discrete math binomial theorem problem: computing the sum

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