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\[ {\large \frac{1^2 + 2^2}{1 \cdot 2} + \frac{2^2 + 3^2}{ 2 \cdot 3} + . . . + \frac{1003^2 + 1004^2}{ 1003 \cdot 1004} + \frac{1004^2 + 1005^2}{1004 \cdot 1005}} \]

What is the nearest integer in the simplified form of the expression above?

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