$A = \frac{1}{3^{2}} + \frac{1}{4^{2}} + \frac{1}{5^{2}} + ... + \frac{1}{49^{2}} + \frac{1}{50^{2}}$
$\Rightarrow A > \frac{1}{3.4} + \frac{1}{4.5} + \frac{1}{5.6} + ... + \frac{1}{49.50} + \frac{1}{50.51}$ $\Rightarrow A > \frac{1}{3} - \frac{1}{4} + \frac{1}{4} - \frac{1}{5} + \frac{1}{5} - \frac{1}{6} + ... + \frac{1}{49} - \frac{1}{50} + \frac{1}{50} - \frac{1}{51}$
$\Rightarrow A > \frac{1}{3} - \frac{1}{51} = \frac{16}{51} > \frac{1}{4}$
