Kết quả của phép tính (-2).(-1 1/2).(-1 1/3)........(-1 1/2009).(-1 1/2010) = ?
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=-2. \(\left(\frac{-3}{2}\right).\left(\frac{-4}{3}\right).....\left(\frac{-2010}{2009}\right).\left(\frac{-2011}{2010}\right)\)
=\(\frac{\left(-2\right).\left(-3\right).\left(-4\right).....\left(-2010\right).\left(-2011\right)}{1.2.3.....2009.2010}\)
=\(\frac{\left(-1\right).\left(-1\right).\left(-1\right).....\left(-1\right).\left(-1\right).\left(-2011\right)}{1.1.1.....1.1}\)
=\(\frac{\left(-1\right)^{2009}.\left(-2011\right)}{1}\)
=\(\frac{\left(-1\right).\left(-2011\right)}{1}=\frac{2011}{1}=2011\)
\(\left(-2\right)\left(-1\frac{1}{2}\right)...........\left(-1\frac{1}{2010}\right)=\frac{\left[\left(-2\right)\left(-3\right).....\left(-2010\right)\right].\left(-2011\right)}{\left(2.3.4.............2010\right)}=\frac{\left(-1\right)\left(-2011\right)}{1}=2011\)
\(\left(-2\right).\left(-1\frac{1}{2}\right).\left(-1\frac{1}{3}\right)....\left(-1\frac{1}{2009}\right).\left(-1\frac{1}{2010}\right)=\left(-2\right).\left(-\frac{3}{2}\right).\left(-\frac{4}{3}\right)....\left(-\frac{2010}{2009}\right).\left(-\frac{2011}{2010}\right)=\frac{\left(-2\right).\left(-3\right).\left(-4\right)....\left(-2010\right).\left(-2011\right)}{2.3.4....2009.2010}\)=2011
-2(-3/2) (-4/3) ...(-2010/2009) (-2011/2010) (co 2010 so hang )
=2011