có 1 / 2^2 < 1/1×2 = 1/1 - 1/2
1 / 3^2 < 1/2 ×3 = 1/2 - 1/3
1/4^2 < 1/3 × 4= 1 /3 - 1 /4
..................................................................
1/ 50 ^ 2 < 1/49×50=1/49 × 1 / 50
=> (1/1^2+1/2^2+1/3^2+1/4^2+....+1/50^2) < 1/1 - 1 / 2 + 1/2 - 1/3 +1/3 -1 /4 +...+1/49 - 1/50
=> A < 1/1 - 1/50
=>A < 49 / 50 <2
=> A < 2