Question

Demonstrati ca $\frac{1}{k(k+1)}$ = $\frac{1}{k}$ - $\frac{1}{k+1}$

Answer 1

$\displaystyle \frac{1}{k(k+1)}= \frac{(k+1)-k}{k(k+1)}= \frac{k+1}{k(k+1)}- \frac{k}{k(k+1)}= \frac{1}{k}- \frac{1}{k+1} .$