Đặt 1/2^2 + 1/3^2 + 1/4^2 + ... + 1/100^2 = A.
Ta có:
1/2^2 < 1/1 . 2
....   
1/100^2 < 1/99 . 100
=> A < 1/1 . 2 + 1/2. 3 + 1/3 . 4 + ... + 1/99 . 100
=> A < 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/99 - 1/100
=> A < 1/1 - 1/100
=> A < 99/100
mà 99/100 < 1.
=> A < 1.
Vậy...