Question

\(\left(1-\frac{1}{2}\right)\)\(\cdot\left(1-\frac{1}{3}\right)\cdot\left(1-\frac{1}{4}\right)\cdot...\cdot\left(1-\frac{1}{9999}\right)\cdot\left(1-\frac{1}{2000}\right)\)

Tính bằng cách nhanh nhất nha mọi người !! 

Answer 1

\(=\left[\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot...\cdot\frac{9998}{9999}\right]\cdot\frac{1999}{2000}=\frac{1\cdot2\cdot3\cdot4\cdot...\cdot9998}{2\cdot3\cdot4\cdot5\cdot...\cdot9999}\cdot\frac{1999}{2000}=\frac{1}{9999}\cdot\frac{1999}{2000}=\frac{1}{2000}\)

Answer 2

=\(\frac{1}{2}\). \(\frac{2}{3}\).\(\frac{3}{4}\)... \(\frac{1999}{2000}\)

=\(\frac{1}{2}\)- \(\frac{1999}{2000}\)

= \(\frac{-999}{2000}\)

Answer 3

Nguyễn Ngọc Linh bạn làm sai rồi :))