A= 1/2 mũ 2 + 1/3 mũ 2+......+ 1/2012 mũ 2 + 1/2013 mũ 2 chúng tỏ A<1

Vì `1/(2^2) < 1/(1.2)`

     `1/(3^2) < 1/(2.3)`

       ............

      `1/(2012^2) < 1/(2011.2012)`

       `1/(2013^2) < 1/(2012.2013)`

`=> A < 1/(1.2) + 1/(2.3) + ... + 1/(2011.2012) + 1/(2012.2013)`

`=> A < 1 - 1/2 + 1/2 - 1/3 + ... + 1/(2011) - 1/(2012) + 1/(2012) - 1/(2013)`

`=> A < 1 - 1/(2013) < 1`

`=> A < 1` (đpcm)