Ta có:
\(\frac{2^2}{3^2}>\frac{2^2}{2009^2}\)
\(\frac{2^2}{5^2}>\frac{2^2}{2009^2}\)
\(\frac{2^2}{7^2}>\frac{2^2}{2009^2}\)
.........
\(\frac{2^2}{2009^2}=\frac{2^2}{2009^2}\)
\(\Rightarrow\frac{2^2}{3^2}+\frac{2^2}{5^2}+\frac{2^2}{7^2}+...+\frac{2^2}{2009^2}>\frac{2^2}{2009^2}+\frac{2^2}{2009^2}+\frac{2^2}{2009^2}+...+\frac{2^2}{2009^2}=\frac{2^2.1004}{2009^2}=\frac{4016}{2009^2}\)(1004 phân số \(\frac{2^2}{2009^2}\)) . Mà:
\(\frac{4016}{2009^2}< 3\)
=> A < 3