Question

Aratati ca 1 pe n-1 pe n+1=1 pe n ori(n+1),oricare ar fi n este numar natural mai mare ca 0

Answer 1

[tex] \frac{1}{n}- \frac{1}{n+1}=\\ amplificam\ prima\ fractie \ cu\ (n+1)\ si\ pe\ a\ doua\ cu\ (n)\\ =\frac{1(n+1)}{n(n+1)}- \frac{1*n}{(n+1)*n}= \frac{n+1-n}{n(n+1)}=\frac{1}{n(n+1)}\\[/tex]

Answer 2

$\frac{1}{n}-\frac{1}{n+1}=\frac{n+1}{n*(n+1)}-\frac{n}{n*(n+1)}=\frac{n+1-n}{n*(n+1)}=\frac{1}{n*(n+1)}$