Question

C= (1/2-1)x(1/3-1)x(1/4-1)x...x(1/2006-1)x(1/2007-1)

Answer 1

Ta có:\(C=\left(\dfrac{1}{2}-1\right)\times\left(\dfrac{1}{3}-1\right)\times\left(\dfrac{1}{4}-1\right)\times...\times\left(\dfrac{1}{2006}-1\right)\times\left(\dfrac{1}{2007}-1\right)\)

   \(=\dfrac{-1}{2}\times\dfrac{-2}{3}\times\dfrac{-3}{4}\times...\times\dfrac{-2005}{2006}\times\dfrac{-2006}{2007}\)

   \(=\dfrac{1}{2007}\) 

Answer 2

Ta có: \(C=\left(\dfrac{1}{2}-1\right)\left(\dfrac{1}{3}-1\right)\cdot...\cdot\left(\dfrac{1}{2006}-1\right)\left(\dfrac{1}{2007}-1\right)\)

\(=\dfrac{-1}{2}\cdot\dfrac{-2}{3}\cdot\dfrac{-3}{4}\cdot...\cdot\dfrac{-2005}{2006}\cdot\dfrac{-2006}{2007}\)

\(=\dfrac{1}{2007}\)