# Let a=1^2/1+2^2/3+3^2/5+....1001^2/2001, b=1^2/3+2^2/5+3^2/7+...+1001^2/2003 then a-b=?

$a - b$
=1^2/1+(2^2-1^2)/3+(3^2-2^2)/5+..... +(1001^2-1000^2)/2001-1001^2/2003
$= 1001 - {1001}^{2} / 2003 = \frac{1001 \cdot 1002}{2003}$
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