A Long Sum

Algebra Level 3

The sum $\frac{3}{1^2 2^2} + \frac{5}{2^2 3^2} + \frac{7}{3^2 4^2} + \cdots + \frac{41}{20^2 21^2}$ can be written as $\dfrac{a}{b}$ where $a$ and $b$ are positive coprime integers. Find $a + b$ .