Question

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Answer 1

=-2. \(\left(\frac{-3}{2}\right).\left(\frac{-4}{3}\right).....\left(\frac{-2010}{2009}\right).\left(\frac{-2011}{2010}\right)\)

=\(\frac{\left(-2\right).\left(-3\right).\left(-4\right).....\left(-2010\right).\left(-2011\right)}{1.2.3.....2009.2010}\)

=\(\frac{\left(-1\right).\left(-1\right).\left(-1\right).....\left(-1\right).\left(-1\right).\left(-2011\right)}{1.1.1.....1.1}\)

=\(\frac{\left(-1\right)^{2009}.\left(-2011\right)}{1}\)

=\(\frac{\left(-1\right).\left(-2011\right)}{1}=\frac{2011}{1}=2011\)