2002 Math OSK, Number 19

Algebra Level pending

Suppose \[a\quad =\quad \frac { { 1 }^{ 2 } }{ 1 } \quad +\quad \frac { { 2 }^{ 2 } }{ 3 } \quad +\quad \frac { { 3 }^{ 2 } }{ 5 } \quad +\quad ...\quad +\quad \frac { { 1001 }^{ 2 } }{ 2001 } \] and \[b\quad =\quad \frac { { 1 }^{ 2 } }{ 3 } \quad +\quad \frac { { 2 }^{ 2 } }{ 5 } \quad +\quad \frac { { 3 }^{ 2 } }{ 7 } \quad +\quad ...\quad +\quad \frac { { 1001 }^{ 2 } }{ 2003 } \] Determine the integer with the closest value to \(a\quad -\quad b\)

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