Question

Answer 1

\(\left(\dfrac{1}{2}-1\right)\left(\dfrac{1}{3}-1\right)\left(\dfrac{1}{4}-1\right)...\left(\dfrac{1}{2008}-1\right)\left(\dfrac{1}{2009}-1\right)\\ \\ \\ \\ =\left(-\dfrac{1}{2}\right)\left(-\dfrac{2}{3}\right)\left(-\dfrac{3}{4}\right)...\left(-\dfrac{2007}{2008}\right)\left(-\dfrac{2008}{2009}\right)\\ \\ \\ \\ =\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot\dfrac{3}{4}\cdot...\cdot\dfrac{2007}{2008}\cdot\dfrac{2008}{2009}\)

( Vì số thừa số là chẵn)

\(=\dfrac{1\cdot2\cdot3\cdot...\cdot2007\cdot2008}{2\cdot3\cdot4\cdot...\cdot2008\cdot2009}\\ \\ \\ \\ =\dfrac{1}{2009}\)