`A=1/4+1/16+1/36+1/64+1/100+1/144+1/196+1/256+1/324`
`A=1/2^2+1/4^2+1/6^2+1/8^2+1/10^2+1/12^2+1/14^2+1/16^2`
`A<1/(2^2-1)+1/(4^2-1)+1/(6^2-1)+1/(8^2-1)+1/(10^2-1)+1/(12^2-1)+1/(14^2-1)+1/(16^2-1)`
`A<1/1.3+1/3.5+1/5.7+1/7.9+1/9.11+1/11.13+1/13.15+1/15.17+1/17.19`
`A<1/2(2/1.3+2/3.5+2/5.7+2/7.9+2/9.11+2/11.13+2/13.15+2/15.17+2/17.19)`
`A<1/2(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13+1/13-1/15+1/15-1/19)`
`A<1/2(1-1/19)<1/2`
`A<1/2`
Vậy `A<1/2`.