I could just start cutting them off

Algebra Level 4

\[ a = \dfrac{1^2}{1} + \dfrac{2^2}{3} + \dfrac{3^2}{5}+\ldots + \dfrac{1001^2}{2001}\\ b = \dfrac{1^2}{3} + \dfrac{2^2}{5} + \dfrac{3^2}{7}+\ldots+ \dfrac{1001^2}{2003}\]

Define \(a,b\) as above. What is the closest integer to \((a- b)\)?

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