Ta có : A=1/4^2+1/6^2+1/8^2+......1/(2n)^2
=1/2^2.(1/2^2+1/3^2+1/4^2+......1/n^2)
Vì 1/2^2<1/2
1/3^2<1/3
1/4^2<1/4
1/n^2<1/(n-1).n
=>1/2^2+1/3^2+1/4^2+......1/n^2<1/2+1/3+1/4+......1/(n-1).n
=>1/2^2+1/3^2+1/4^2+......1/n^2<1-1/2 +1/2 -1/3+1/3-1/4+1/4+......+1/(n-1)-1/n
=>1/2^2+1/3^2+1/4^2+......1/n^2<1-1/n
=>1/2^2.(1/2^2+1/3^2+1/4^2+......1/n^2<1.1/4
=>A<1/4