Question

Why is $\lim\limits_{x \to \infty} \frac{(\sqrt{x})!}{(\sqrt{x+1})!}$ = 1 and not 0?

score 98 · Answer 1 · 2022-04-10 23:58:42

98

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Why is $\lim\limits_{x \to \infty} \frac{(\sqrt{x})!}{(\sqrt{x+1})!}$ = 1 and not 0?

Published on 10 Apr 2022 - 23:58

score 139 · Answer 2 · 2026-04-14 00:11:22

139

Views

$P(A_i) = \frac{1}{n} = \frac{(n-1)!}{n!} $

Published on 14 Apr 2026 - 0:11

score 152 · Answer 3 · 2026-04-09 03:33:12

152

Views

How to prove Pascal's identity?

Published on 09 Apr 2026 - 3:33

score 47 · Answer 4 · 2026-04-06 05:18:28

47

Views

Somehow the last digit of 6x7x8 or 16x17x18 is the same as 3!, can someone prove this pattern for me?

Published on 06 Apr 2026 - 5:18

score 59 · Answer 5 · 2022-04-13 14:34:36

59

Views

Spivak Calculus, Ch 10, problem 32b: Can we use Leibniz's formula to calculate $f^{(k)}(x)$ if $f(x)=\frac{1}{x^2-1}$?

Published on 13 Apr 2022 - 14:34

score 92 · Answer 6 · 2026-04-14 00:59:59

92

Views

How Many Ways to Pick Objects : So That No One Picks the Exact Same Objects?

Published on 14 Apr 2026 - 0:59

score 32 · Answer 7 · 2026-04-13 07:05:03

32

Views

Expansion of factorial as linear combination of binomial coefficients

Published on 13 Apr 2026 - 7:05

score 248 · Answer 8 · 2022-04-18 08:28:59

248

Views

Proving the factorial integral using induction

Published on 18 Apr 2022 - 8:28

score 105 · Answer 9 · 2026-04-13 14:46:24

105

Views

Factorial as a product of three consecutive natural numbers

Published on 13 Apr 2026 - 14:46

score 59 · Answer 10 · 2026-04-11 11:31:36

59

Views

How do you solve this factorial problem

Published on 11 Apr 2026 - 11:31

score 75 · Answer 11 · 2026-04-10 16:13:42

75

Views

Questions in combinatorics involving the sum of a few series

Published on 10 Apr 2026 - 16:13

score 44 · Answer 12 · 2026-04-10 11:04:32

44

Views

How do we handle the factorials in the binomials/choice numbers?

Published on 10 Apr 2026 - 11:04

score 20 · Answer 13 · 2022-04-25 08:55:08

20

Views

Ski jump result combinations

Published on 25 Apr 2022 - 8:55

score 55 · Answer 14 · 2026-04-14 05:07:59

55

Views

Sum of factorials in 3D symmetrical random walk $\sum_{k=0}^n\binom{n}{k}^2\binom{2(n-k)}{n-k}$

Published on 14 Apr 2026 - 5:07

score 162 · Answer 15 · 2026-04-11 00:29:55

162

Views

Finding the maximum $k$ such that $(7!)!$ is divisible by $(7!)^{k!}\cdot(6!)!$

Published on 11 Apr 2026 - 0:29

List Question

Why is $\lim\limits_{x \to \infty} \frac{(\sqrt{x})!}{(\sqrt{x+1})!}$ = 1 and not 0?

$P(A_i) = \frac{1}{n} = \frac{(n-1)!}{n!} $

How to prove Pascal's identity?

Somehow the last digit of 6x7x8 or 16x17x18 is the same as 3!, can someone prove this pattern for me?

Spivak Calculus, Ch 10, problem 32b: Can we use Leibniz's formula to calculate $f^{(k)}(x)$ if $f(x)=\frac{1}{x^2-1}$?

How Many Ways to Pick Objects : So That No One Picks the Exact Same Objects?

Expansion of factorial as linear combination of binomial coefficients

Proving the factorial integral using induction

Factorial as a product of three consecutive natural numbers

How do you solve this factorial problem

Questions in combinatorics involving the sum of a few series

How do we handle the factorials in the binomials/choice numbers?

Ski jump result combinations

Sum of factorials in 3D symmetrical random walk $\sum_{k=0}^n\binom{n}{k}^2\binom{2(n-k)}{n-k}$

Finding the maximum $k$ such that $(7!)!$ is divisible by $(7!)^{k!}\cdot(6!)!$

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