cho A= 1/1^2+1/2^2+1/3^2+1/4^2+….+1/50^2 chứng minh A<2

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