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\(\left(-2\right)\left(-1\frac{1}{2}\right)\left(-1\frac{1}{3}\right)....\left(-1\frac{1}{2010}\right)=-2.\frac{-3}{2}.\frac{-4}{3}...\frac{-2011}{2010}=2.\frac{3}{2}.\frac{4}{3}...\frac{2011}{2010}\)
=2011
\(\left(-2\right)\left(-1\frac{1}{2}\right)...........\left(-1\frac{1}{2010}\right)=\frac{\left[\left(-2\right)\left(-3\right).....\left(-2010\right)\right].\left(-2011\right)}{\left(2.3.4.............2010\right)}=\frac{\left(-1\right)\left(-2011\right)}{1}=2011\)
\(\left(-2\right).\left(-1\frac{1}{2}\right).\left(-1\frac{1}{3}\right)....\left(-1\frac{1}{2009}\right).\left(-1\frac{1}{2010}\right)=\left(-2\right).\left(-\frac{3}{2}\right).\left(-\frac{4}{3}\right)....\left(-\frac{2010}{2009}\right).\left(-\frac{2011}{2010}\right)=\frac{\left(-2\right).\left(-3\right).\left(-4\right)....\left(-2010\right).\left(-2011\right)}{2.3.4....2009.2010}\)=2011