Question

Cum rezolvi ecuatia (n+2)! +(n+1)! =35n!

Answer 1

1*2*...*(n+1)*(n+2) + 1*2*...*(n+1) = 35*n!
(n+1)! * (n+2) + (n+1)! = 35*n!
(n+1)! * (n+2+1) = 35*n!
(n+1)! * (n+3) = 35*n!
n! * (n+1) * (n+3) = 35*n!
(n+1)*(n+3) = 35
35=5*7 descompunere in factori primi
n+1=5 si n+3=7
n=4