ta có: 1/3^2<1/2.3</p>
1/4^2<1/3.4</p>
1/5^2<1/4.5</p>
........................................
1/100^2<1/99.100</p>
=> 1/3^2+1/3+1/4^2+...+1/100^2<1/2.3+1/3.4+1/4.5+...+1/99.100</p>
1/3^2+1/3+1/4^2+...+1/100^2< 1/2-1/3+1/3-1/4+...+1/99-1/100
1/3^2+1/3+1/4^2+...+1/100^2< 1/2-1/100
vì 1/2-1/100 < 1/2
nên 1/3^2+1/3+1/4^2+...+1/100^2<1/2</p>