Question

Find the smallest value of $n$ so that the greater potency of $5$ which divides $n!$ is $5^{84}$. What are the other numbers that enjoy this property?

score 95 · Answer 1 · 2026-04-02 11:21:24

95

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Find the smallest value of $n$ so that the greater potency of $5$ which divides $n!$ is $5^{84}$. What are the other numbers that enjoy this property?

Published on 02 Apr 2026 - 11:21

score 130 · Answer 2 · 2026-04-02 11:15:15

130

Views

If $N$ is a multiple of $100$, $N!$ ends with $\left(\frac{N}4-1 \right)$ zeroes.

Published on 02 Apr 2026 - 11:15

score 192 · Answer 3 · 2026-04-02 11:16:11

192

Views

Show that there is no natural number $n$ such that $3^7$ is the largest power of $3$ dividing $n!$

Published on 02 Apr 2026 - 11:16

score 54 · Answer 4 · 2013-11-20 18:35:36

54

Views

show that if $m,n\in\mathbb{N}$ are such that $(m,n)=1$, then $\frac{(m+n-1)!}{m!n!}\in\mathbb{N}.$

Published on 20 Nov 2013 - 18:35

score 8.9k · Answer 5 · 2013-11-21 00:23:30

8.9k

Views

Factorial lower bound: $n! \ge {\left(\frac n2\right)}^{\frac n2}$

Published on 21 Nov 2013 - 0:23

score 7.9k · Answer 6 · 2013-11-21 16:08:15

7.9k

Views

Need help understanding the factorial formula $n!=n(n-1)(n-2)\cdots(3)(2)(1)$

Published on 21 Nov 2013 - 16:08

score 5.6k · Answer 7 · 2013-11-21 18:29:44

5.6k

Views

Use a factorial argument to show that $C(2n,n+1)+C(2n,n)=\frac{1}{2}C(2n+2,n+1)$

Published on 21 Nov 2013 - 18:29

score 593 · Answer 8 · 2013-11-22 02:32:30

593

Views

Series -- Coefficient Cn and Radius of Convergence

Published on 22 Nov 2013 - 2:32

score 169 · Answer 9 · 2013-11-22 09:50:39

169

Views

prove that $(\frac{n}{3})^n<n!<e\cdot(\frac{n}{2})^n$

Published on 22 Nov 2013 - 9:50

score 283 · Answer 10 · 2013-11-22 22:23:48

283

Views

Proving a sequence with induction reasoning

Published on 22 Nov 2013 - 22:23

score 259 · Answer 11 · 2013-11-23 19:26:05

259

Views

How to solve this summation: $\sum_{k=1}^{n}\frac{k2^{k}}{(k+2)!}$

Published on 23 Nov 2013 - 19:26

score 667 · Answer 12 · 2013-11-24 22:33:53

667

Views

Compute the limit $\lim_{n \to \infty} \frac{n!}{n^n}$

Published on 24 Nov 2013 - 22:33

score 139 · Answer 13 · 2013-11-25 05:19:52

139

Views

Is $\sum_{n=1}^{\infty}\frac{2^nn!}{(n+1)!}$ absolutely convergent?

Published on 25 Nov 2013 - 5:19

score 402 · Answer 14 · 2013-11-25 06:01:40

402

Views

Proving $2^n<n!$ using simple induction.

Published on 25 Nov 2013 - 6:01

score 639 · Answer 15 · 2013-11-25 06:59:43

639

Views

Solve Algebraical.ly $0.5=\dfrac{365!}{365^{n}(365-n)!} $

Published on 25 Nov 2013 - 6:59

List Question

Find the smallest value of $n$ so that the greater potency of $5$ which divides $n!$ is $5^{84}$. What are the other numbers that enjoy this property?

If $N$ is a multiple of $100$, $N!$ ends with $\left(\frac{N}4-1 \right)$ zeroes.

Show that there is no natural number $n$ such that $3^7$ is the largest power of $3$ dividing $n!$

show that if $m,n\in\mathbb{N}$ are such that $(m,n)=1$, then $\frac{(m+n-1)!}{m!n!}\in\mathbb{N}.$

Factorial lower bound: $n! \ge {\left(\frac n2\right)}^{\frac n2}$

Need help understanding the factorial formula $n!=n(n-1)(n-2)\cdots(3)(2)(1)$

Use a factorial argument to show that $C(2n,n+1)+C(2n,n)=\frac{1}{2}C(2n+2,n+1)$

Series -- Coefficient Cn and Radius of Convergence

prove that $(\frac{n}{3})^n<n!<e\cdot(\frac{n}{2})^n$

Proving a sequence with induction reasoning

How to solve this summation: $\sum_{k=1}^{n}\frac{k2^{k}}{(k+2)!}$

Compute the limit $\lim_{n \to \infty} \frac{n!}{n^n}$

Is $\sum_{n=1}^{\infty}\frac{2^nn!}{(n+1)!}$ absolutely convergent?

Proving $2^n<n!$ using simple induction.

Solve Algebraical.ly $0.5=\dfrac{365!}{365^{n}(365-n)!} $

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