Question

Tính nhanh \(A=\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)...\left(\frac{1}{2015}-1\right)\)

Answer 1

\(A=\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)\cdot...\cdot\left(\frac{1}{2015}-1\right)=\frac{1}{2}\cdot\frac{2}{3}\cdot...\cdot\frac{2014}{2015}=\frac{1\cdot2\cdot3\cdot...\cdot2013\cdot2014}{2\cdot3\cdot...\cdot2014\cdot2015}=\frac{1}{2015}\)

Answer 2

\(A=\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)...\left(\frac{1}{2015}-1\right)=-\frac{1}{2}.\frac{-2}{3}...\frac{-2014}{2015}=\frac{1}{2015}\)

Answer 3

vậy -1 hay là 1