Question

Question based on binomial theorem and complex numbers.

score 277 · Answer 1 · 2026-03-27 05:34:32

277

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Question based on binomial theorem and complex numbers.

Published on 27 Mar 2026 - 5:34

score 114 · Answer 2 · 2018-12-02 03:10:57

114

Views

Prove that if $\binom{n}{k}$ = $\binom{n}{k+1}$, then $n$ must be odd

Published on 02 Dec 2018 - 3:10

score 295 · Answer 3 · 2026-03-22 08:46:35

295

Views

Proof of Identity to Zero of the Sum of a Product of Binomial Coefficients & Pochhammer Numbers

Published on 22 Mar 2026 - 8:46

score 123 · Answer 4 · 2018-12-03 21:41:28

123

Views

identities and binomial coefficients

Published on 03 Dec 2018 - 21:41

score 167 · Answer 5 · 2026-03-25 10:58:52

167

Views

Proof of a Binomial expression summation

Published on 25 Mar 2026 - 10:58

score 85 · Answer 6 · 2018-12-04 12:29:01

85

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Proving that $\sum_{k=0}^n{(-1)^k\over k+1}\binom{n}{k}={1\over n+1}$

Published on 04 Dec 2018 - 12:29

score 591 · Answer 7 · 2026-03-26 06:32:36

591

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Prove that $(1-x)^n \leq 1 -xn+\frac{n(n-1)}{2}x^2$ when $0\leq x\leq 1$ and $n\geq2$

Published on 26 Mar 2026 - 6:32

score 133 · Answer 8 · 2026-03-26 06:25:31

133

Views

Proof Ideas - Strong Induction, Pascal's Triangle and Fibonacci Numbers

Published on 26 Mar 2026 - 6:25

score 81 · Answer 9 · 2026-03-25 20:52:08

81

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value of $k$ in binomial expression

Published on 25 Mar 2026 - 20:52

score 2.4k · Answer 10 · 2018-12-06 10:59:08

2.4k

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A simple finite combinatorial sum I found, that seems to work, would have good reasons to work, but I can't find in the literature.

Published on 06 Dec 2018 - 10:59

score 61 · Answer 11 · 2026-03-26 06:28:44

61

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Root of a plynomial in (0,1)

Published on 26 Mar 2026 - 6:28

score 56 · Answer 12 · 2026-03-22 11:34:07

56

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Let n belongs to +ve integer and $(1+x+x^2)^n=\sum_{r=0}^{2n} {a_rx^r}$ prove that: $a_r=a_{0<r<2n}$

Published on 22 Mar 2026 - 11:34

score 92 · Answer 13 · 2018-12-07 05:35:09

92

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sum of $\sum^{n}_{k=0}(-1)^k\cdot \frac{\binom{n}{k}}{\binom{k+3}{k}}$

Published on 07 Dec 2018 - 5:35

score 1.2k · Answer 14 · 2026-03-27 03:43:20

1.2k

Views

What is the coefficient of $x^{11}$ in $(3x-9)^{19}$?

Published on 27 Mar 2026 - 3:43

score 431 · Answer 15 · 2018-12-08 19:13:41

431

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Prove the identity $\sum_{k=0}^{n}\sum_{r=0}^{k} \binom{k}{r} \binom{n}{k} = 3^n$

Published on 08 Dec 2018 - 19:13

List Question

Question based on binomial theorem and complex numbers.

Prove that if $\binom{n}{k}$ = $\binom{n}{k+1}$, then $n$ must be odd

Proof of Identity to Zero of the Sum of a Product of Binomial Coefficients & Pochhammer Numbers

identities and binomial coefficients

Proof of a Binomial expression summation

Proving that $\sum_{k=0}^n{(-1)^k\over k+1}\binom{n}{k}={1\over n+1}$

Prove that $(1-x)^n \leq 1 -xn+\frac{n(n-1)}{2}x^2$ when $0\leq x\leq 1$ and $n\geq2$

Proof Ideas - Strong Induction, Pascal's Triangle and Fibonacci Numbers

value of $k$ in binomial expression

A simple finite combinatorial sum I found, that seems to work, would have good reasons to work, but I can't find in the literature.

Root of a plynomial in (0,1)

Let n belongs to +ve integer and $(1+x+x^2)^n=\sum_{r=0}^{2n} {a_rx^r}$ prove that: $a_r=a_{0<r<2n}$

sum of $\sum^{n}_{k=0}(-1)^k\cdot \frac{\binom{n}{k}}{\binom{k+3}{k}}$

What is the coefficient of $x^{11}$ in $(3x-9)^{19}$?

Prove the identity $\sum_{k=0}^{n}\sum_{r=0}^{k} \binom{k}{r} \binom{n}{k} = 3^n$

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