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Constrained multinomial theorem removing terms from sum

score 200 · Answer 1 · 2026-03-26 21:25:33

200

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Constrained multinomial theorem removing terms from sum

Published on 26 Mar 2026 - 21:25

score 46 · Answer 2 · 2022-08-17 08:29:45

46

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How to solve $f(n) = \frac{9}{2}f(n-1) + \frac{9}{2}f(n-2) - \frac{81}{2}f(n-3) + \frac{81}{2}f(n-4) + n + 2$

Published on 17 Aug 2022 - 8:29

score 125 · Answer 3 · 2026-03-28 20:14:24

125

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Showing that $\sum_{k=0}^{n}{m+k\choose m}^{-1}=\frac{m}{m-1}\left[1-{m+n\choose m-1}^{-1}\right],m>1.$

Published on 28 Mar 2026 - 20:14

score 72 · Answer 4 · 2026-04-06 00:17:23

72

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Rationale for validity of the binomial expansion involving rational powers

Published on 06 Apr 2026 - 0:17

score 145 · Answer 5 · 2022-08-26 05:08:39

145

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Is there any method to compute $\frac{d^{n}}{d x^{n}}\left(\cos ^{k} x\right)$ other than complex numbers?

Published on 26 Aug 2022 - 5:08

score 18 · Answer 6 · 2026-03-17 06:32:37

18

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COMBINATORICS: Number of parking possibilities.

Published on 17 Mar 2026 - 6:32

score 100 · Answer 7 · 2022-08-30 04:58:06

100

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Combinatorial proof of $(x+y)_{(n)} = \sum_k \binom n k x_{(k)}y_{(n-k)}$

Published on 30 Aug 2022 - 4:58

score 19 · Answer 8 · 2026-03-23 20:02:48

19

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How to effectively show the following expression equals zero using the binomial theorem

Published on 23 Mar 2026 - 20:02

score 82 · Answer 9 · 2022-09-11 13:08:14

82

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if $f(x) = x+2/(1\cdot3)x^3+2\cdot4/(1\cdot3\cdot5)x^5+\cdots$ comment on the value of $f(1/2)$

Published on 11 Sep 2022 - 13:08

score 118 · Answer 10 · 2026-04-05 07:16:27

118

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Sum of binomial distribution with increasing trials

Published on 05 Apr 2026 - 7:16

score 73 · Answer 11 · 2022-09-13 04:14:54

73

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Evaluation of $~\Delta\left\{\sum_{k=0}^{20}(-1)^{k}\binom{40}{2k}x^{40-2k}y^{2k}\right\}$

Published on 13 Sep 2022 - 4:14

score 57 · Answer 12 · 2022-09-14 05:20:48

57

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Evaluating $\sum_{k=a}^{15} \frac{k!}{(k-a)!}$ for $0 \leq a \leq 15$

Published on 14 Sep 2022 - 5:20

score 126 · Answer 13 · 2022-09-27 17:13:14

126

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how to calculate the value $0.9^{31}$

Published on 27 Sep 2022 - 17:13

score 138 · Answer 14 · 2026-03-26 18:58:52

138

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Having difficulties with pendulum theory and percentage error homework problem.

Published on 26 Mar 2026 - 18:58

score 238 · Answer 15 · 2022-10-05 03:30:19

238

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Let $p$ be an odd prime and let $n$ be a positive integer. Use the Binomial Theorem to show that $(1+p)^{p^{n-2}}\not\equiv1$ (mod $p^n$).

Published on 05 Oct 2022 - 3:30

List Question

Constrained multinomial theorem removing terms from sum

How to solve $f(n) = \frac{9}{2}f(n-1) + \frac{9}{2}f(n-2) - \frac{81}{2}f(n-3) + \frac{81}{2}f(n-4) + n + 2$

Showing that $\sum_{k=0}^{n}{m+k\choose m}^{-1}=\frac{m}{m-1}\left[1-{m+n\choose m-1}^{-1}\right],m>1.$

Rationale for validity of the binomial expansion involving rational powers

Is there any method to compute $\frac{d^{n}}{d x^{n}}\left(\cos ^{k} x\right)$ other than complex numbers?

COMBINATORICS: Number of parking possibilities.

Combinatorial proof of $(x+y)_{(n)} = \sum_k \binom n k x_{(k)}y_{(n-k)}$

How to effectively show the following expression equals zero using the binomial theorem

if $f(x) = x+2/(1\cdot3)x^3+2\cdot4/(1\cdot3\cdot5)x^5+\cdots$ comment on the value of $f(1/2)$

Sum of binomial distribution with increasing trials

Evaluation of $~\Delta\left\{\sum_{k=0}^{20}(-1)^{k}\binom{40}{2k}x^{40-2k}y^{2k}\right\}$

Evaluating $\sum_{k=a}^{15} \frac{k!}{(k-a)!}$ for $0 \leq a \leq 15$

how to calculate the value $0.9^{31}$

Having difficulties with pendulum theory and percentage error homework problem.

Let $p$ be an odd prime and let $n$ be a positive integer. Use the Binomial Theorem to show that $(1+p)^{p^{n-2}}\not\equiv1$ (mod $p^n$).

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