Question

[pham thi thu hien]

1, tính nhanh:

(1-1/2) *(1-1/3) *(1-1/4)* (1-1/5)*......*(1-1/2003)*(1-1/2004)

Answer 1

[Khổng Mai Linh]

(1-1/2)x(1-1/3)x(1-1/4)x(1-1/5)x.......x (1-1/2003)x(1-1/2004)

=1/2 x 2/3 x 3/4 x 4/5 x.....x2002/2003 x 2003/2004

=\(\frac{1\times2\times3\times4\times...\times2002\times2003}{2\times3\times4\times5....\times2003\times2004}\)

=\(\frac{1}{2004}\)

Answer 2

[Nguyễn Phạm Hồng Anh]

\(\left(1-\frac{1}{2}\right)x\left(1-\frac{1}{3}\right)x\left(1-\frac{1}{4}\right)x\left(1-\frac{1}{5}\right)x...x\left(1-\frac{1}{2003}\right)x\left(1-\frac{1}{2004}\right)\)

\(=\frac{1}{2}x\frac{2}{3}x\frac{3}{4}x\frac{4}{5}x...x\frac{2002}{2003}x\frac{2003}{2004}\)

 \(=\frac{1x2x3x4x....x2002x2003}{2x3x4x5x...x2003x2004}\)

   \(=\frac{1}{2004}\)