Calculus Help!!!?

Question

The last problem in my summer math packet was made for a genius so if you r one please show me how to solve it. thanks

(3(n+1)!)/(5n!)

Answer 1

Note, as an example, 4! / 3!
= 4.3.2.1 / 3.2.1
= 4
General rule is (n + 1)! / n! = n + 1
3 (n + 1)! / 5 n! = (3 / 5) (n + 1)

Answer 2

(n+1)!=(n+1)(n+1-1)!
= (n+1)(n)!
3(n+1)!/5(n!) =3(n+1)(n!)/5n!
cancelling n!
=3(n+1)/5

Answer 3

(3(n+1)!)/(5n!)

= (3(n+1)(n)!/(5n!)

= (3(n+1)/5)