Question

Salut , ajutati-ma va rog! Sa se calculeze : (n+2)! / n! + (n+1)! ? va rog explicati-mi! Multumesc

Answer 1

$\dfrac{(n+2)!}{n!+(n+1)!} = \dfrac{n!(n+1)(n+2)}{n!+n!(n+1)} = \dfrac{n!(n+1)(n+2)}{n!\Big[1+(n+1)\Big]} = \\ \\ = \dfrac{n!(n+1)(n+2)}{n!(n+2)} = \dfrac{(n+1)(n+2)}{n+2} = n+1$