The numbers $\frac{1}{1}, \frac{1}{2}, \ldots, \frac{1}{2010}$ are written on a blackboard. A student chooses any two of the numbers, say $x$ and $y$, erases them, and then writes down $x + y + xy$. He continues this process until only one number remains on the blackboard. What is this number?

Let's think step by step and output the final answer within \boxed{}.
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