Question

Rút gọn biểu thức

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

Answer 1

\(\left(1-\dfrac{1}{2}\right).\left(1-\dfrac{1}{3}\right).............\left(1-\dfrac{1}{2014}\right)\)

\(=\left(\dfrac{2}{2}-\dfrac{1}{2}\right).\left(\dfrac{3}{3}-\dfrac{1}{3}\right)..............\left(\dfrac{2014}{2014}-\dfrac{1}{2014}\right)\)

\(=\dfrac{1}{2}.\dfrac{2}{3}................\dfrac{2013}{2014}\)

\(=\dfrac{1}{2014}\)

Answer 2

\(\left(1-\dfrac{1}{2}\right).\left(1-\dfrac{1}{3}\right)....\left(1-\dfrac{1}{2014}\right)\)

\(=\left(\dfrac{2}{2}-\dfrac{1}{2}\right).\left(\dfrac{3}{3}-\dfrac{1}{3}\right).....\left(\dfrac{2014}{2014}-\dfrac{1}{2014}\right)\)

\(=\dfrac{1}{2}.\dfrac{2}{3}.....\dfrac{2013}{2014}\)

\(=\dfrac{1}{2014}\)

Chúc bạn học tốt!