How do I prove this statement?

[Darya]

n!(n!-1)!=(n!)!

I've tried to do stuff with putting n! into the parentheses but it did nothing. Any ideas about how I could start better? Thanks.

 

[MarkFL]

To make it easier to see, let \(m=n!\) and we have:

[MATH]m(m-1)!=m![/MATH]

 

[Mr. Bland]

Observe that [MATH]n![/MATH] differs from [MATH](n-1)![/MATH] by a factor of [MATH]n[/MATH], such that [MATH]n(n - 1)! = n![/MATH]
How can you leverage this fact to prove the original statement?

 

[Darya]

To make it easier to see, let \(m=n!\) and we have:

[MATH]m(m-1)!=m![/MATH]

That made me instantly realize it, thank you so much for help!!!!

 

[Darya]

Observe that [MATH]n![/MATH] differs from [MATH](n-1)![/MATH] by a factor of [MATH]n[/MATH], such that [MATH]n(n - 1)! = n![/MATH]
How can you leverage this fact to prove the original statement?

Got it, thanks for your help!!!