Question

A simplificação da expressão (n + 1)! - n! + (n - 1)! / n!
Preciso urgente, valeu

Answer 1

Observe que:

$(n+1)!=(n+1)n(n-1)!$

$n!=n(n-1)!$

Assim, $(n+1)!-n!+(n-1)!=(n-1)![(n+1)n-n+1]$

Logo:

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

ou seja, $\dfrac{(n+1)n-n+1}{n}=\dfrac{n^2+n-n+1}{n}=\dfrac{n^2+1}{n}$