\(=\left(1+\frac{1}{2}\right)\cdot\left(1+\frac{1}{3}\right)\cdot\left(1+\frac{1}{4}\right)\cdot....\cdot\left(1+\frac{1}{2010}\right)\)
\(=\frac{3}{2}\cdot\frac{4}{3}\cdot\frac{5}{4}\cdot...\cdot\frac{2011}{2010}\)
\(=\frac{3\cdot4\cdot5\cdot...\cdot2011}{2\cdot3\cdot4\cdot...\cdot2010}\)
\(=\frac{2011}{2}\)
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