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Differences in Values

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April 2, 2013

Problem Statement

Let a=121+223+325+⋯+100122001a=\dfrac{1^2}1+\dfrac{2^2}3+\dfrac{3^2}5+\cdots+\dfrac{1001^2}{2001} and b=123+225+327+⋯+100122003.b=\dfrac{1^2}3+\dfrac{2^2}5+\dfrac{3^2}7+\cdots+\dfrac{1001^2}{2003}. Find the integer closest to a−ba-b.
<spanclass=′latex−bold′>(A)</span>500<spanclass=′latex−bold′>(B)</span>501<spanclass=′latex−bold′>(C)</span>999<spanclass=′latex−bold′>(D)</span>1000<spanclass=′latex−bold′>(E)</span>1001<span class='latex-bold'>(A) </span>500\qquad<span class='latex-bold'>(B) </span>501\qquad<span class='latex-bold'>(C) </span>999\qquad<span class='latex-bold'>(D) </span>1000\qquad<span class='latex-bold'>(E) </span>1001
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