Question

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

Answer 1

`=1/2 xx 2/3 xx 3/4 xx...xx 2002/2003 xx 2003/2004`

`=1/2004`

Answer 2

`(1-1/2)xx(1-1/3)xx.......xx(1-1/2003)xx(1-1/2004)`

`=(2/2-1/2)xx(3/3-1/3)xx....xx(2003/2003 - 1/2003)xx(2004/2004-1/2004)`

`=1/2 xx 2/3 xx ..... xx 2002/2003 xx 2003/2004`

`=(1xx2xx.....xx2002)/(2xx3xx.....xx2004)`

`=1/2004`

Answer 3

$=\frac{1}{2}\times \frac{2}{3}\times \frac{3}{4}\times ...\times \frac{2002}{2003}\times \frac{2003}{2004}$

$=\frac{1}{2004}$