Докажите равенство: 1) n! + (n+1)! = n! (n+2) 2) (n-1)! + n! + (n+1)! = (n+1)^2 * (n-1)!

Question

Докажите равенство:
1) n! + (n+1)! = n! (n+2)
2) (n-1)! + n! + (n+1)! = (n+1)^2 * (n-1)!

Answer 1

N! + (n+1)! = n! + n! * (n+1) = n!(1 + (n +1) = n!(n + 2)

(n-1)! + n! + (n+1)! = (n-1)! + n * (n-1)! + (n+1)!  =
= (n-1)! *(1 +n) + (n-1)! *n * (n+1) = (n+1) * ((n-1)! + (n-1)! *n))=
=(n+1) * (n-1)! * (1+ n) = (n-1)! * (n+1)^2