(1-2/1)+(2/1-3/1)+(3/1-4/1)…+（2009/1-2010/1)=

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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