Ta có: 1/22< 1/1.2=1-1/2
1/32<1/2.3=1/2-1/3
..............................
1/1002< 1/99.100=1/99-1/100
Do đó: 1+1/22+1/32+...+1/1002< 1+1-1/2+1/2-1/3+....+1/99-1/100
=> 1+1/22+1/32+....+1/1002<1+1-1/100=2-1/100<2
nên 1+1/22+1/32+....+1/1002<2
Vậy 1+1/22+1/32+...+1/1002<2