Question

A simplificação da expressão (n+1)!-n!(n-1)!/n! resulta em:

Answer 1

$\dfrac{(n+1)!-n!.(n-1)!}{n!}=\dfrac{(n+1)!}{n!}-\dfrac{\not n!.(n-1)!}{\not n!} \\ \\ \\ \dfrac{(n+1).\not n!}{\not n!} - (n-1)!= \boxed{(n+1)-(n-1)!}$