Newbetuts

How to prove that $\sum\limits_{n=1}^{\infty}\frac{1}{n(n+1)(n+2)...(n+k)} = \frac{1}{kk!}$ for every $k\geqslant1$

Solving $n!+m!+k^2=n!m!$ for positive integers $n,m,k$

Find the sum of the digits in the number 100!

What remainder does $34!$ leave when divided by $71$?

Help with difficult telescoping series question: $\frac3{1!+2!+3!}+\frac4{2!+3!+4!}+\ldots+\frac{2012}{2010!+2011!+2012!}$ [duplicate]

Some trouble with the induction

Is Ramanujan's approximation for the factorial optimal, or can it be tweaked? (answer below)

Prove $\sum_{n=1}^\infty(e-\sum_{k=0}^n\frac1{k!})=1$

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

Factorial number of digits

Limits to infinity of a factorial function: $\lim_{n\to\infty}\frac{n!}{n^{n/2}}$

How do I solve this divisibility problem?

How to prove the sum of combination is equal to $2^n - 1$

Showing $\lim_{n \to +\infty} \log(n!)/(n\log n) = 1$ without using Stirling approximation

If $n = 51! +1$, then find number of primes among $n+1,n+2,\ldots, n+50$

Showing $f(kx,ky)\geq f(x,y)$

$n!$ as product of consecutive numbers

New posts in factorial

What is the remainder left after dividing $1! + 2! + 3! + ... + 100!$ by $5$?

Simplifying sum with rising and falling factorials

Why is $\log(n!)$ $O(n\log n)$?

How to prove that $\sum\limits_{n=1}^{\infty}\frac{1}{n(n+1)(n+2)...(n+k)} = \frac{1}{kk!}$ for every $k\geqslant1$

Solving $n!+m!+k^2=n!m!$ for positive integers $n,m,k$

Find the sum of the digits in the number 100!

What remainder does $34!$ leave when divided by $71$?

Help with difficult telescoping series question: $\frac3{1!+2!+3!}+\frac4{2!+3!+4!}+\ldots+\frac{2012}{2010!+2011!+2012!}$ [duplicate]

Some trouble with the induction

Is Ramanujan's approximation for the factorial optimal, or can it be tweaked? (answer below)

Prove $\sum_{n=1}^\infty(e-\sum_{k=0}^n\frac1{k!})=1$

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

Factorial number of digits

Limits to infinity of a factorial function: $\lim_{n\to\infty}\frac{n!}{n^{n/2}}$

How do I solve this divisibility problem?

How to prove the sum of combination is equal to $2^n - 1$

Showing $\lim_{n \to +\infty} \log(n!)/(n\log n) = 1$ without using Stirling approximation

If $n = 51! +1$, then find number of primes among $n+1,n+2,\ldots, n+50$

Showing $f(kx,ky)\geq f(x,y)$

$n!$ as product of consecutive numbers