Tính: (1-1/2x1/2)x(1-1/3x1/3)x(1-1/4x1/4)x…x(1-1/2007x1/2007)

* Hướng dẫn giải

(1-$\frac{1}{2}$x$\frac{1}{2}$)x(1-$\frac{1}{3}$x$\frac{1}{3}$)x(1-$\frac{1}{4}$x$\frac{1}{4}$)x…x(1-$\frac{1}{2007}$x$\frac{1}{2007}$)
= ( 1 - $\frac{1}{4}$) x ( 1 - $\frac{1}{9}$) x ( 1- $\frac{1}{16}$) x .....x ( 1 - $\frac{1}{4028049}$)
= $\frac{3}{4}$ x $\frac{8}{9}$ x $\frac{15}{16}$ x .....x $\frac{4028048}{4028049}$
= 3 x 8 x 15 x .....x $\frac{4028048}{4}$ x 9 x 16 x ......x 4028049
= 1 x 3 x 2 x 4 x 3 x 5 x .....x 2006 x $\frac{2008}{2}$x2 x 3 x3 x 4 x 4 x .....x 2007 x 2007
= ( 1 x 2 x 3 x .....x 2006) x $\frac{( 3 x 4 x 5 x .....x 2008)}{( 2 x 3 x 4 x ....x 2007)}$x ( 2 x 3 x 4 x ....x 2007)
= $\frac{2008}{2007}$ x 2
= $\frac{1004}{2007}$