`A=1/4+1/16+1/36+...+1/10000`
`=>4A=1+1/4+1/9+...+1/2500`
`=>4A=1+1/2.2+1/3.3+...+1/50.50`
`=>4A<1+1/1.2+1/2.3+...+1/49.50`
`=>4A<1+1-1/2+1/2-1/3+...+1/49-1/50`
`=>4A<1+1-1/50`
`=>4A<1+49/50`
`=>4A<99/50`
`=>A<99/200<100/200=1/2`
`=>A<1/2`
Vậy giá trị biểu thức bé hơn `1/2`.