I sense a pattern!

Algebra Level 2

1221+1421+1621+1821++1100021  \dfrac{1}{2^{2}-1}+\dfrac{1}{4^{2}-1}+\dfrac{1}{6^{2}-1}+\dfrac{1}{8^{2}-1}+\cdots+\dfrac{1}{1000^{2}-1}\

The value of the sum above can be expressed as ab,\frac{a}{b}, where aa and bb are coprime positive integers. Find the value of a+ba+b.

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