Question

Arătaţi că:$\frac{1}{n*(n+1)}= \frac{1}{n}- \frac{1}{n+1}$.

Answer 1

Facem de la dreapta la stânga.
$\frac{1}{n}-\frac{1}{n+1}=\frac{n+1}{n(n+1)}-\frac{n}{n(n+1)}=\frac{n+1-n}{n(n+1)}=\frac{1}{n(n+1)}$

Answer 2

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