Chứng minh rằng A = (1/3 ² ) + (1/4 ² ) + (1/5 ² ) + …. + (1/49 ² ) + (1/50 ² ) > (1/4)

$A = \frac{1}{3^{2}} + \frac{1}{4^{2}} + \frac{1}{5^{2}} + … + \frac{1}{49^{2}} + \frac{1}{50^{2}}$

$\Rightarrow A > \frac{1}{3.4} + \frac{1}{4.5} + \frac{1}{5.6} + … + \frac{1}{49.50} + \frac{1}{50.51}$ $\Rightarrow A > \frac{1}{3} – \frac{1}{4} + \frac{1}{4} – \frac{1}{5} + \frac{1}{5} – \frac{1}{6} + … + \frac{1}{49} – \frac{1}{50} + \frac{1}{50} – \frac{1}{51}$

$\Rightarrow A > \frac{1}{3} – \frac{1}{51} = \frac{16}{51} > \frac{1}{4}$