Question

Evaluate $\frac{0!}{4!}+\frac{1!}{5!}+\frac{2!}{6!}+\frac{3!}{7!}+\frac{4!}{8!}+\cdots$

score 1.7k · Answer 1 · 2016-06-13 15:30:22

1.7k

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Evaluate $\frac{0!}{4!}+\frac{1!}{5!}+\frac{2!}{6!}+\frac{3!}{7!}+\frac{4!}{8!}+\cdots$

Published on 13 Jun 2016 - 15:30

score 101 · Answer 2 · 2016-06-14 04:31:17

101

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Maybe this inequality holds? $x!-y!>x^n$?

Published on 14 Jun 2016 - 4:31

score 2.6k · Answer 3 · 2016-06-14 10:18:45

2.6k

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Expanding a factorial

Published on 14 Jun 2016 - 10:18

score 144 · Answer 4 · 2016-06-17 14:04:54

144

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Tight lower bound on falling factorial

Published on 17 Jun 2016 - 14:04

score 1k · Answer 5 · 2026-04-02 10:32:49

1k

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The divergent sum of alternating factorials

Published on 02 Apr 2026 - 10:32

score 111 · Answer 6 · 2016-06-20 16:37:19

111

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How to find the Summation of series of Factorials?

Published on 20 Jun 2016 - 16:37

score 436 · Answer 7 · 2016-06-21 02:02:28

436

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Can Euler's generalization of factorial be done for double factorial?

Published on 21 Jun 2016 - 2:02

score 670 · Answer 8 · 2016-06-21 02:30:35

670

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Seeking closed form for infinite sum $\sum \limits_{ n=1 }^{ \infty }{ \frac { { \left(n! \right) }^{ 2 } }{ { n }^{ 3 }(2n)! } }$

Published on 21 Jun 2016 - 2:30

score 991 · Answer 9 · 2016-06-24 03:05:42

991

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Restrictions on Factorial Usage

Published on 24 Jun 2016 - 3:05

score 436 · Answer 10 · 2016-06-24 21:06:06

436

Views

Why does $(128)!$ equal the product of these binomial coefficients $128! = \binom{128}{64}\binom{64}{32}^2 \dots \binom21^{64}$?

Published on 24 Jun 2016 - 21:06

score 931 · Answer 11 · 2016-06-25 03:22:47

931

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Perfect square from a multiple of factorials

Published on 25 Jun 2016 - 3:22

score 747 · Answer 12 · 2026-03-30 00:04:13

747

Views

Conjecture about primes and the factorial: for all primes $p>5$, must there exist a prime $q<p$ such that $q\equiv m!\pmod p$ for some $2<m<p$?

Published on 30 Mar 2026 - 0:04

score 137 · Answer 13 · 2026-03-29 23:57:30

137

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Conjecture concerning modular arithmetic

Published on 29 Mar 2026 - 23:57

score 1.5k · Answer 14 · 2016-06-27 13:08:00

1.5k

Views

Find last 5 significant digits of 2017!

Published on 27 Jun 2016 - 13:08

score 159 · Answer 15 · 2026-03-28 11:35:27

159

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Find the divisors of $5040$ in the Plato's dialogue "Theaetetus"

Published on 28 Mar 2026 - 11:35

List Question

Evaluate $\frac{0!}{4!}+\frac{1!}{5!}+\frac{2!}{6!}+\frac{3!}{7!}+\frac{4!}{8!}+\cdots$

Maybe this inequality holds? $x!-y!>x^n$?

Expanding a factorial

Tight lower bound on falling factorial

The divergent sum of alternating factorials

How to find the Summation of series of Factorials?

Can Euler's generalization of factorial be done for double factorial?

Seeking closed form for infinite sum $\sum \limits_{ n=1 }^{ \infty }{ \frac { { \left(n! \right) }^{ 2 } }{ { n }^{ 3 }(2n)! } }$

Restrictions on Factorial Usage

Why does $(128)!$ equal the product of these binomial coefficients $128! = \binom{128}{64}\binom{64}{32}^2 \dots \binom21^{64}$?

Perfect square from a multiple of factorials

Conjecture about primes and the factorial: for all primes $p>5$, must there exist a prime $q<p$ such that $q\equiv m!\pmod p$ for some $2<m<p$?

Conjecture concerning modular arithmetic

Find last 5 significant digits of 2017!

Find the divisors of $5040$ in the Plato's dialogue "Theaetetus"

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