Question

6. (UA-AM) Simplifique a expressão: (n+1)!+n! /(n+2)!, (n€Nn>1)

Answer 1

$\mathsf{\dfrac{(n+1)!+n!}{(n+2)!}}$

$\mathsf{\dfrac{(n+1).n!+n!}{(n+2)(n+1).n!}}$

$\mathsf{\dfrac{n!(n+1+1)}{(n+2)(n+1).n!}}$

$\mathsf{\dfrac{\cancel{n!}\cancel{(n+2)}}{\cancel{(n+2)}(n+1).\cancel{n!}}=\dfrac{1}{n+1}}$