Simplify:

2/1! - 3/2! + 4/3! - 5/4! + ... + 2010/2009! - 2011/2010!, where k! denotes the product of all integers from 1 up to k, that is,
1! = 1,
2! = 1x2 = 2,
3! = 1x2x3 = 6, and so on.

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