Question

$\frac{4}{1*5} + \frac{4}{5*9} + \frac{4}{9*13} + ... + \frac{4}{101*105} = ?$
Va rog dau funda

Answer 1

$\frac{4}{1*5} = \frac{5-1}{1*5} = \frac{5}{1*5}- \frac{1}{1*5}=1- \frac{1}{5}$
4/5*9=9-5/5*9=9/5*9 -5/5*9=1/5 -1/9
...
$\frac{4}{101*105}= \frac{1}{101} - \frac{1}{105}$
1- 1/5 +1/5 -1/9+ ....+1/101-1/105 = 1-1/105 =104/105