Question

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

score 184 · Answer 1 · 2026-04-17 15:52:23

184

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

Published on 17 Apr 2026 - 15:52

score 158 · Answer 2 · 2026-04-16 11:19:24

158

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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 16 Apr 2026 - 11:19

score 591 · Answer 3 · 2026-04-12 10:10:41

591

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Summations: Rewriting the Binomial Theorem

Published on 12 Apr 2026 - 10:10

score 283 · Answer 4 · 2026-04-29 12:50:48

283

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

Published on 29 Apr 2026 - 12:50

score 318 · Answer 5 · 2026-05-06 09:50:30

318

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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 06 May 2026 - 9:50

score 848 · Answer 6 · 2026-05-06 14:45:14

848

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

Published on 06 May 2026 - 14:45

score 358 · Answer 7 · 2026-05-06 14:20:35

358

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Binomial coefficient: Search for multiples of 13

Published on 06 May 2026 - 14:20

score 189 · Answer 8 · 2026-04-15 01:20:13

189

Views

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

Published on 15 Apr 2026 - 1:20

score 79 · Answer 9 · 2026-04-15 16:56:05

79

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

Published on 15 Apr 2026 - 16:56

score 574 · Answer 10 · 2026-04-16 20:53:49

574

Views

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

Published on 16 Apr 2026 - 20:53

score 970 · Answer 11 · 2026-04-16 06:20:02

970

Views

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

Published on 16 Apr 2026 - 6:20

score 72 · Answer 12 · 2026-04-16 23:19:51

72

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 16 Apr 2026 - 23:19

score 1.1k · Answer 13 · 2026-03-25 07:53:19

1.1k

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

Published on 25 Mar 2026 - 7:53

score 340 · Answer 14 · 2026-04-10 19:02:14

340

Views

Distinct terms in multinomial expansion

Published on 10 Apr 2026 - 19:02

score 379 · Answer 15 · 2026-04-11 12:11:31

379

Views

Combinatorial Proofs for Summations: A Possible Generalisation?

Published on 11 Apr 2026 - 12:11

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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