Question

number of distinct terms in binomial expansion of $\left(x+x^{-1}+x^2+x^{-2}\right)^{15}$

score 181 · Answer 1 · 2018-02-13 02:44:49

181

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number of distinct terms in binomial expansion of $\left(x+x^{-1}+x^2+x^{-2}\right)^{15}$

Published on 13 Feb 2018 - 2:44

score 155 · Answer 2 · 2018-02-14 00:49:57

155

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Random Variables Proof $P(Y_1+Y_2+Y_3+...+Y_n=k)=\frac 1 {m^n} \sum (-1)^i \binom{n}{i} \binom{k-mi-1}{n-1}$ using binomial theorem

Published on 14 Feb 2018 - 0:49

score 588 · Answer 3 · 2018-02-14 15:06:23

588

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Summations: Rewriting the Binomial Theorem

Published on 14 Feb 2018 - 15:06

score 282 · Answer 4 · 2026-03-25 01:18:09

282

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How many rational numbers are in the opening of this binomial: $(\sqrt3+\sqrt[3]2)^{100}$

Published on 25 Mar 2026 - 1:18

score 316 · Answer 5 · 2026-03-20 07:47:07

316

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If $n$ is a multiple of $8$, then the number of sets of size divisible by $4$ is $2^{n-2} + 2^{(n-2)/2}$

Published on 20 Mar 2026 - 7:47

score 846 · Answer 6 · 2026-03-20 05:35:23

846

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Determine the coefficient of $x^6$ in $(1 - x)^{15}$

Published on 20 Mar 2026 - 5:35

score 356 · Answer 7 · 2026-03-19 23:15:45

356

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Binomial coefficient: Search for multiples of 13

Published on 19 Mar 2026 - 23:15

score 188 · Answer 8 · 2026-03-25 03:24:08

188

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Binomial expansion on $\sqrt{1+\frac{4}{x^2}+\frac{1}{x^3}}$

Published on 25 Mar 2026 - 3:24

score 76 · Answer 9 · 2018-02-23 17:25:26

76

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Show for all positive integers l : $0 = \sum_{k=0}^ {3l-1} (-3)^{k} { 6l \choose 2k+1}$

Published on 23 Feb 2018 - 17:25

score 570 · Answer 10 · 2026-03-22 00:56:59

570

Views

Evaluate $(-\sqrt3 + i)^9$

Published on 22 Mar 2026 - 0:56

score 967 · Answer 11 · 2018-02-25 19:01:18

967

Views

Flipping the coin until either head or tail has occurred 10 times

Published on 25 Feb 2018 - 19:01

score 69 · Answer 12 · 2018-02-26 19:29:54

69

Views

Prove that $\forall n \in \Bbb{N}, 1 <n, \left( 1 + \frac{1}{n} \right)^n < \sum_{i=0}^n \frac{1}{i!}$

Published on 26 Feb 2018 - 19:29

score 1.1k · Answer 13 · 2026-03-23 16:29:29

1.1k

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The sum $\sum_{r=0}^{20}r(20-r)\binom{20}{r}^2$

Published on 23 Mar 2026 - 16:29

score 336 · Answer 14 · 2018-03-01 04:10:33

336

Views

Distinct terms in multinomial expansion

Published on 01 Mar 2018 - 4:10

score 376 · Answer 15 · 2018-03-01 07:15:00

376

Views

Combinatorial Proofs for Summations: A Possible Generalisation?

Published on 01 Mar 2018 - 7:15

List Question

number of distinct terms in binomial expansion of $\left(x+x^{-1}+x^2+x^{-2}\right)^{15}$

Random Variables Proof $P(Y_1+Y_2+Y_3+...+Y_n=k)=\frac 1 {m^n} \sum (-1)^i \binom{n}{i} \binom{k-mi-1}{n-1}$ using binomial theorem

Summations: Rewriting the Binomial Theorem

How many rational numbers are in the opening of this binomial: $(\sqrt3+\sqrt[3]2)^{100}$

If $n$ is a multiple of $8$, then the number of sets of size divisible by $4$ is $2^{n-2} + 2^{(n-2)/2}$

Determine the coefficient of $x^6$ in $(1 - x)^{15}$

Binomial coefficient: Search for multiples of 13

Binomial expansion on $\sqrt{1+\frac{4}{x^2}+\frac{1}{x^3}}$

Show for all positive integers l : $0 = \sum_{k=0}^ {3l-1} (-3)^{k} { 6l \choose 2k+1}$

Evaluate $(-\sqrt3 + i)^9$

Flipping the coin until either head or tail has occurred 10 times

Prove that $\forall n \in \Bbb{N}, 1 <n, \left( 1 + \frac{1}{n} \right)^n < \sum_{i=0}^n \frac{1}{i!}$

The sum $\sum_{r=0}^{20}r(20-r)\binom{20}{r}^2$

Distinct terms in multinomial expansion

Combinatorial Proofs for Summations: A Possible Generalisation?

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