Pierādīt, ka

\(\frac{1}{1^{4}+1^{2}+1}+\frac{2}{2^{4}+2^{2}+1}+\frac{3}{3^{4}+3^{2}+1}+\ldots+\frac{2009}{2009^{4}+2009^{2}+1}<\frac{1}{2}\).