Question

Simplifique (n+1)! - n!/ n! + (n-1)!​

Answer 1

(n+1)! - n!/ n! + (n-1)!

(n+1).n! - n!/ n.(n-1)! + (n-1)!

n!(n+1 - 1) / (n-1)!(n +n-1)

n!(n) / (n-1)!(2n-1)

n(n-1)!.n / (n-1)!.(2n-1)

n²/2n-1

Answer 2

Resposta:

n²/2n-1

Explicação passo-a-passo:

(n+1)! – n!/n!+ (n+1)! =

(n+1).n! - n!/n.(n-1)! + (n-1)! =

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

n!(n) /(n-1)! .(2n-1) =

n(n-1)!.n /(n-1)!.(2n-1)=

n² /2n-1