Question

Evaluating the power series of the multifactorial reciprocal $\sum_{n=0}^\infty \frac{x^n}{n!!...!!}$

score 158 · Answer 1 · 2020-07-18 14:46:48

158

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Evaluating the power series of the multifactorial reciprocal $\sum_{n=0}^\infty \frac{x^n}{n!!...!!}$

Published on 18 Jul 2020 - 14:46

score 234 · Answer 2 · 2020-07-20 04:09:21

234

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When trying to find the number of unique pairs in $n$ elements why does the combination formula output a different value from $n(n-1)/2$

Published on 20 Jul 2020 - 4:09

score 146 · Answer 3 · 2020-07-22 20:37:02

146

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Is there a function that grows slower than the factorial function and whose derivative grows faster than the function itself?

Published on 22 Jul 2020 - 20:37

score 100 · Answer 4 · 2020-07-23 05:24:31

100

Views

Prove that $\frac{d^n}{dx^n}(1-e^x)^n\Big\rvert_{x=0}=(-1)^nn!$

Published on 23 Jul 2020 - 5:24

score 102 · Answer 5 · 2020-07-27 01:12:14

102

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Prove: $(n-1)! \equiv -1 \pmod{n}$

Published on 27 Jul 2020 - 1:12

score 484 · Answer 6 · 2020-07-28 18:59:47

484

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Is $n!\alpha \bmod 1$ dense in $[0,1]$?

Published on 28 Jul 2020 - 18:59

score 126 · Answer 7 · 2020-07-28 20:43:58

126

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factorial divided by a smaller factorial to the n power

Published on 28 Jul 2020 - 20:43

score 166 · Answer 8 · 2020-07-29 03:12:07

166

Views

The sum of difference products related to determinants with factorials

Published on 29 Jul 2020 - 3:12

score 135 · Answer 9 · 2020-07-29 03:52:06

135

Views

Is there a closed form of $\sum_{n=0}^{\infty} \frac{(-1)^n}{(4n+1)!!}$?

Published on 29 Jul 2020 - 3:52

score 424 · Answer 10 · 2026-03-29 08:56:06

424

Views

How to prove Stirling's formula. Using Wallis formula

Published on 29 Mar 2026 - 8:56

score 174 · Answer 11 · 2016-07-05 19:43:17

174

Views

Closed-from for the series: $\sum_{k=0}^{\infty} \frac{1}{(k!)!}$

Published on 05 Jul 2016 - 19:43

score 266 · Answer 12 · 2016-07-05 20:21:18

From $ \frac{\left(n\cdot \:n!+1\right)\left(n+1\right)}{\left(n+1\right)\left(n+1\right)!+1} $ to $ \frac{n+\frac{1}{n!}}{n+1+\frac{1}{n!}} $?

score 197 · Answer 13 · 2016-07-06 21:10:07

197

Views

Finding the remainder of an exhausted $m!$

Published on 06 Jul 2016 - 21:10

score 1k · Answer 14 · 2016-07-06 23:00:38

1k

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Factorial Proof by Induction Question: $ \frac1{2!} + \frac2{3!} + \dots+ \frac{n}{(n+1)!} = 1 - \frac1{(n+1)!} $?

Published on 06 Jul 2016 - 23:00

score 255 · Answer 15 · 2016-07-10 13:17:50

255

Views

Find all nonnegative integers $m$ and $n$ such that $m!+1=n^2$.

Published on 10 Jul 2016 - 13:17

List Question

Evaluating the power series of the multifactorial reciprocal $\sum_{n=0}^\infty \frac{x^n}{n!!...!!}$

When trying to find the number of unique pairs in $n$ elements why does the combination formula output a different value from $n(n-1)/2$

Is there a function that grows slower than the factorial function and whose derivative grows faster than the function itself?

Prove that $\frac{d^n}{dx^n}(1-e^x)^n\Big\rvert_{x=0}=(-1)^nn!$

Prove: $(n-1)! \equiv -1 \pmod{n}$

Is $n!\alpha \bmod 1$ dense in $[0,1]$?

factorial divided by a smaller factorial to the n power

The sum of difference products related to determinants with factorials

Is there a closed form of $\sum_{n=0}^{\infty} \frac{(-1)^n}{(4n+1)!!}$?

How to prove Stirling's formula. Using Wallis formula

Closed-from for the series: $\sum_{k=0}^{\infty} \frac{1}{(k!)!}$

From $ \frac{\left(n\cdot \:n!+1\right)\left(n+1\right)}{\left(n+1\right)\left(n+1\right)!+1} $ to $ \frac{n+\frac{1}{n!}}{n+1+\frac{1}{n!}} $?

Finding the remainder of an exhausted $m!$

Factorial Proof by Induction Question: $ \frac1{2!} + \frac2{3!} + \dots+ \frac{n}{(n+1)!} = 1 - \frac1{(n+1)!} $?

Find all nonnegative integers $m$ and $n$ such that $m!+1=n^2$.

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