# 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 $$a + b$$.

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