Question

Alguém me ajuda pelo amor de deus

Simplifique as expressões:

a) n! / (n - 1)!

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

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

Answer 1

Resposta:

Explicação passo a passo:

$a)\frac{n!}{(n-1)!} =\frac{n!}{(n-1).n!} =\frac{1}{n-1} \\\\b)\frac{n!-(n+1)!}{n!} =\frac{n!-(n+1)n!}{n!} =\frac{n![1-(n+1)]}{n!} =1-n-1=-n\\\\c)\frac{[(n+2)!+(n+1)(n-1)!}{{(n+1)(n-1)!}} =\frac{(n+2)(n+1)n(n-1)!+(n+1)(n-1)!}{(n+1)(n-1)!}=\frac{(n+1)(n-1)![(n+2)n+1]}{(n+1)(n-1)!} =\\\\n^2+2n+1$