Question

[bi bi]

A= (1-1/2)x(1-1/3)x(1-1/4)x.........x(1-1/2013)x(1-1/2014)

Answer 1

[nghia]

\(A=\left(1-\frac{1}{2}\right)x\left(1-\frac{1}{3}\right)x......x\left(1-\frac{1}{2013}\right)x\left(1-\frac{1}{2014}\right)\)

\(A=\frac{1}{2}x\frac{2}{3}x\frac{3}{4}x...............x\frac{2012}{2013}x\frac{2013}{2014}\)

\(A=\frac{1}{2014}\)

Answer 2

[Đào Trọng Luân]

\(\left[1-\frac{1}{2}\right]\left[1-\frac{1}{3}\right]...\left[1-\frac{1}{2014}\right]\)

\(=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}...\cdot\frac{2013}{2014}\)

\(=\frac{1\cdot2\cdot3\cdot...\cdot2013}{2\cdot3\cdot4\cdot5\cdot...\cdot2014}=\frac{1}{2014}\)