\(\frac{1}{1^2}+\frac{1}{3^2}+\frac{1}{5^2}+....+\frac{1}{99^2}\)
\(< \frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+.....+\frac{1}{98\cdot99}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+....+\frac{1}{98}-\frac{1}{99}\)
\(=1-\frac{1}{99}\)
\(< 1\)
\(< \frac{5}{4}\)