Question

VALENDO 25 PONTOS!!! URGENTE

Qual a simplificação de [tex] \frac{1}{(n+1)!} + \frac{n-1}{n!}



RESPOSTA : n^2 /(n+1)!

Answer 1

$\frac{1}{(n+1)!} + \frac{n-1}{n!} =\frac{1}{(n+1)!}+\frac{n-1}{n(n-1)(n-2)!}=\frac{1}{(n+1)!}+\frac{1}{n(n-2)!}=$ $\frac{n(n-2)!+(n+1)!}{(n+1)!n(n-2)!}=\frac{n(n-2)!+(n+1)n(n-1)(n-2)!}{(n+1)!n(n-2)!}=\frac{n(n-2)!(1+(n+1)(n-1))}{(n+1)!n(n-2)!}=$ $\frac{1+(n+1)(n-1)}{(n+1)!}=\frac{1+n^2-1}{(n=1)!}=\frac{n^2}{(n+1)!}$