ta có
1/2.3+1/3.4+...+1/2016.2017<1/2^2+1/3^2+1/4^2+...+1/2016^2
<=>1/2-1/3+1/3-1/4+...+1/2016-1/2017<1/2^2+1/3^2+1/4^2+...+1/2016^2
<=>1/2-1/2017<1/2^2+1/3^2+1/4^2+...+1/2016^2
<=>2015/4034<1/2^2+1/3^2+1/4^2+...+1/2016^2 (1)
ta lại có:
1/2^2+1/3^2+1/4^2+...+1/2016^2<1/1.2+1/2.3+...+1/2015/2016
<=>1/2^2+1/3^2+1/4^2+...+1/2016^2<1-1/2+1/2-1/3+...+1/2015-1/2016
<=>1/2^2+1/3^2+1/4^2+...+1/2016^2<1-1/2016
<=>1/2^2+1/3^2+1/4^2+...+1/2016^2<2015/2016 (2)
từ (1)(2)=> đpcm
