Question 14
Prove the inequality
$$
2010 \lt \frac{2^2 + 1}{2^2 - 1} + \frac{3^2 + 1}{3^2 - 1} + \dots + \frac{2010^2 + 1}{2010^2 - 1} \lt 2010 \frac{1}{2} \quad \text{(Grade 9.)}
$$
$$
2010 \lt \frac{2^2 + 1}{2^2 - 1} + \frac{3^2 + 1}{3^2 - 1} + \dots + \frac{2010^2 + 1}{2010^2 - 1} \lt 2010 \frac{1}{2} \quad \text{(Grade 9.)}
$$