Question

(1) Sum of two factorials in two ways; (2) Value of $a^{2010}+a^{2010}+1$ given $a^4+a^3+a^2+a+1=0$.

score 206 · Answer 1 · 2026-04-03 07:29:16

206

Views

(1) Sum of two factorials in two ways; (2) Value of $a^{2010}+a^{2010}+1$ given $a^4+a^3+a^2+a+1=0$.

Published on 03 Apr 2026 - 7:29

score 414 · Answer 2 · 2017-10-16 14:41:17

414

Views

Let $k$ and $n$ be positive integers, find all pairs $(n,k)$ of positive integers such that $(n+1)^k-1=n!$

Published on 16 Oct 2017 - 14:41

score 325 · Answer 3 · 2026-04-06 21:08:14

325

Views

Reducing combinations in fractions

Published on 06 Apr 2026 - 21:08

score 59 · Answer 4 · 2017-10-18 18:00:53

59

Views

Show that $(n-j)! \leq \frac{n!}{(j+1)!}$

Published on 18 Oct 2017 - 18:00

score 249 · Answer 5 · 2017-10-19 01:21:17

249

Views

How to write $3\times 7\times 11\times \ldots \times (4n-1)$ as a factorial?

Published on 19 Oct 2017 - 1:21

score 1.1k · Answer 6 · 2017-10-20 05:41:51

1.1k

Views

How many arrangements of the letters in the word CANADIAN do not contain a double N?

Published on 20 Oct 2017 - 5:41

score 118 · Answer 7 · 2017-10-21 04:12:57

118

Views

Induction prove $\begin{equation} 2^{n^2} \geq n! \end{equation}$ for a nonnegative integer

Published on 21 Oct 2017 - 4:12

score 245 · Answer 8 · 2017-10-22 14:50:37

245

Views

Calculate $\lim\limits_{n\to\infty}\frac{\ln(n!)}{n\ln(n)}$.

Published on 22 Oct 2017 - 14:50

score 39 · Answer 9 · 2017-10-22 18:11:14

39

Views

Can the given expression be simplified? If yes, How?

Published on 22 Oct 2017 - 18:11

score 1.4k · Answer 10 · 2017-10-23 08:16:54

1.4k

Views

Is there a formal name for the product of the first N primes?

Published on 23 Oct 2017 - 8:16

score 5.8k · Answer 11 · 2026-04-07 23:13:37

5.8k

Views

How to divide large factorial numbers?

Published on 07 Apr 2026 - 23:13

score 736 · Answer 12 · 2026-03-26 21:27:31

736

Views

Compute $N! \ \mathrm{mod}P$ , where $N<=10^9$ and $P=10^9+7$, where $N!$ is $N$ factorial

Published on 26 Mar 2026 - 21:27

score 60 · Answer 13 · 2026-04-08 02:06:59

60

Views

Factorial related sum

Published on 08 Apr 2026 - 2:06

score 253 · Answer 14 · 2017-10-27 19:53:36

253

Views

$\lim\limits_{n\to\infty} \frac {n}{\sqrt[n]{n!}} $ and $\lim\limits_{n\to\infty} C_{2 n}^n$

Published on 27 Oct 2017 - 19:53

score 267 · Answer 15 · 2017-10-28 02:13:01

267

Views

Rearranging a summation of factorials into a Taylor series expansion

Published on 28 Oct 2017 - 2:13

List Question

(1) Sum of two factorials in two ways; (2) Value of $a^{2010}+a^{2010}+1$ given $a^4+a^3+a^2+a+1=0$.

Let $k$ and $n$ be positive integers, find all pairs $(n,k)$ of positive integers such that $(n+1)^k-1=n!$

Reducing combinations in fractions

Show that $(n-j)! \leq \frac{n!}{(j+1)!}$

How to write $3\times 7\times 11\times \ldots \times (4n-1)$ as a factorial?

How many arrangements of the letters in the word CANADIAN do not contain a double N?

Induction prove $\begin{equation} 2^{n^2} \geq n! \end{equation}$ for a nonnegative integer

Calculate $\lim\limits_{n\to\infty}\frac{\ln(n!)}{n\ln(n)}$.

Can the given expression be simplified? If yes, How?

Is there a formal name for the product of the first N primes?

How to divide large factorial numbers?

Compute $N! \ \mathrm{mod}P$ , where $N<=10^9$ and $P=10^9+7$, where $N!$ is $N$ factorial

Factorial related sum

$\lim\limits_{n\to\infty} \frac {n}{\sqrt[n]{n!}} $ and $\lim\limits_{n\to\infty} C_{2 n}^n$

Rearranging a summation of factorials into a Taylor series expansion

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