Ta có:
1/2^2=1/2.2<1/1.2
1/3^2=1/3.3<1/2.3
...........
1/2014^2=1/2014.2014<1/2013.2014
⇒1/2^2+1/3^2+1/4^2+...+1/2014^2 < 1/1.2+1/2.3+1/3.4+...+1/2013.2014
⇒1/2^2+1/3^2+1/4^2+...+1/2014^2 < 1-1/2+1/2-1/3+1/3-1/4+...+1/2013-1/2014
⇒1/2^2+1/3^2+1/4^2+...+1/2014^2 < 1-1/2014
⇒1/2^2+1/3^2+1/4^2+...+1/2014^2 < 2014/2014-1/2014=2013/2014
mà 2013/2014<3/4
nên 1/2^2+1/3^2+1/4^2+...+1/2014^2 < 3/4
chúc bạn học tốt
