The given expression can be simplified as follows:
(1 - 2/1) + (2/1 - 3/1) + (3/1 - 4/1) + ... + (2009/1 - 2010/1)
Simplifying the fractions within each parenthesis, we get:
(1 - 2) + (2 - 3) + (3 - 4) + ... + (2009 - 2010)
Notice that the second term in each parenthesis cancels out with the first term in the next parenthesis, and so on. Hence, we are left with:
1 - 2010
This can be further simplified as:
-2009
Therefore, the sum of the given expression is -2009.
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