Question

Value of $ {_3F_2}{\left(1,n+\frac32,1-r;\frac32,n+2;1\right)} $

score 218 · Answer 1 · 2026-04-15 16:36:43

218

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Value of $ {_3F_2}{\left(1,n+\frac32,1-r;\frac32,n+2;1\right)} $

Published on 15 Apr 2026 - 16:36

score 134 · Answer 2 · 2026-04-16 16:35:06

134

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The coefficient of $x^{101}$ in the expansion of the expression $(5+x)^{500}+x(5+x)^{499}....+x^{500}$ is

Published on 16 Apr 2026 - 16:35

score 54 · Answer 3 · 2026-04-13 08:08:14

54

Views

Binomial coefficient identity with alternating summands

Published on 13 Apr 2026 - 8:08

score 86 · Answer 4 · 2026-04-14 09:05:38

86

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How to prove $\sum_{k=1}^b \frac{\binom{b}{k}}{\binom{r+b}{k}}r = \frac{b}{r + 1}$?

Published on 14 Apr 2026 - 9:05

score 170 · Answer 5 · 2026-04-13 20:51:27

170

Views

Identities using only binomial coefficient

Published on 13 Apr 2026 - 20:51

score 41 · Answer 6 · 2026-04-13 00:02:51

41

Views

Seeking combinatorial proof for an Identity involving $2^{2n}$ and a sum of binomial coefficients

Published on 13 Apr 2026 - 0:02

score 36 · Answer 7 · 2026-04-16 03:55:23

36

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Given $\beta \gt 4$, show that $\lim_{n\to\infty}{{\sum_{k=1}^{n}{k}{n\choose{k}}{n\choose{k-1}} \over{\beta^{n}}}} = 0$

Published on 16 Apr 2026 - 3:55

score 71 · Answer 8 · 2026-04-16 12:26:44

71

Views

Confusion regarding the nth term in a binomial expansion (positive integral index)

Published on 16 Apr 2026 - 12:26

score 52 · Answer 9 · 2026-04-11 09:45:19

52

Views

Can we solve this only by using bijection?

Published on 11 Apr 2026 - 9:45

score 73 · Answer 10 · 2026-04-15 04:17:45

73

Views

Asymptotic of binomial coefficient if $k^2$ = $o(n)$

Published on 15 Apr 2026 - 4:17

score 94 · Answer 11 · 2026-04-10 22:02:52

94

Views

Tips/strategies for bounding this partial sum with binomial coefficients

Published on 10 Apr 2026 - 22:02

score 60 · Answer 12 · 2026-04-13 18:35:44

60

Views

Confusion with $\binom{n}{x}$ = $\binom{n}{y}$

Published on 13 Apr 2026 - 18:35

score 318 · Answer 13 · 2026-04-13 20:48:44

318

Views

A conjecture on representing $\sum\limits_{k=0} ^m (-1)^ka^{m-k}b^k$ as sum of powers of $(a+b)$.

Published on 13 Apr 2026 - 20:48

score 44 · Answer 14 · 2026-04-10 22:09:51

44

Views

Subtract summations with binomials (probability)

Published on 10 Apr 2026 - 22:09

score 47 · Answer 15 · 2026-04-16 23:15:38

47

Views

Proof of sum of somewhat binomial distribution to infinity

Published on 16 Apr 2026 - 23:15

List Question

Value of $ {_3F_2}{\left(1,n+\frac32,1-r;\frac32,n+2;1\right)} $

The coefficient of $x^{101}$ in the expansion of the expression $(5+x)^{500}+x(5+x)^{499}....+x^{500}$ is

Binomial coefficient identity with alternating summands

How to prove $\sum_{k=1}^b \frac{\binom{b}{k}}{\binom{r+b}{k}}r = \frac{b}{r + 1}$?

Identities using only binomial coefficient

Seeking combinatorial proof for an Identity involving $2^{2n}$ and a sum of binomial coefficients

Given $\beta \gt 4$, show that $\lim_{n\to\infty}{{\sum_{k=1}^{n}{k}{n\choose{k}}{n\choose{k-1}} \over{\beta^{n}}}} = 0$

Confusion regarding the nth term in a binomial expansion (positive integral index)

Can we solve this only by using bijection?

Asymptotic of binomial coefficient if $k^2$ = $o(n)$

Tips/strategies for bounding this partial sum with binomial coefficients

Confusion with $\binom{n}{x}$ = $\binom{n}{y}$

A conjecture on representing $\sum\limits_{k=0} ^m (-1)^ka^{m-k}b^k$ as sum of powers of $(a+b)$.

Subtract summations with binomials (probability)

Proof of sum of somewhat binomial distribution to infinity

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