a)=1/2*2/3......*19/20

=1/20

b)=3/2*4/3......*2008/2007

=3/2007

a quên = 3/2008

Ta có:\(C=\left(\dfrac{1}{2}-1\right)\times\left(\dfrac{1}{3}-1\right)\times\left(\dfrac{1}{4}-1\right)\times...\times\left(\dfrac{1}{2006}-1\right)\times\left(\dfrac{1}{2007}-1\right)\)

   \(=\dfrac{-1}{2}\times\dfrac{-2}{3}\times\dfrac{-3}{4}\times...\times\dfrac{-2005}{2006}\times\dfrac{-2006}{2007}\)

   \(=\dfrac{1}{2007}\) 

Ta có: \(C=\left(\dfrac{1}{2}-1\right)\left(\dfrac{1}{3}-1\right)\cdot...\cdot\left(\dfrac{1}{2006}-1\right)\left(\dfrac{1}{2007}-1\right)\)

\(=\dfrac{-1}{2}\cdot\dfrac{-2}{3}\cdot\dfrac{-3}{4}\cdot...\cdot\dfrac{-2005}{2006}\cdot\dfrac{-2006}{2007}\)

\(=\dfrac{1}{2007}\)

Sai thì chịu!

Mình cũng ra là:1/2007.

\(\left(1-\frac{1}{2}\right)x\left(1-\frac{1}{3}\right)x\left(1-\frac{1}{4}\right)x............x\left(1-\frac{1}{2017}\right)\))

= \(\frac{1}{2}x\frac{2}{3}x\frac{3}{4}x..............x\frac{2006}{2007}\)

= \(\frac{1}{2007}\)

Đó là kết quả sau khi trực tiêu

Bài này dễ mà

Trong violympic 

1/2007 đấy

trong violympic đó đúng 100%

(1-1/2x1/2)x(1-1/3x1/3)x(1-1/4x1/4)x…x(1-1/2007x1/2007) = ( 1 - 1/4 ) x ( 1 - 1/9 ) x ( 1- 1/16) x .....x ( 1 - 1/4028049) = 3/4 x 8/9 x 15/16 x .....x 4028048 / 4028049 = 3 x 8 x 15 x .....x 4028048 / 4 x 9 x 16 x ......x 4028049 = 1 x 3 x 2 x 4 x 3 x 5 x .....x 2006 x 2008 / 2x2 x 3 x3 x 4 x 4 x .....x 2007 x 2007 = ( 1 x 2 x 3 x .....x 2006) x ( 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) = 2008 / 2007 x 2 = 1004 / 2007

ta có : (1-1/2)*...*(1-1/2007)

=1/2*2/3*3/4*...*2006/2007

=(1*2*3*4*5*...2006)/(2*3*4*5*...*2007)

=1/2007

vậy kết quả phép tính trên là 1/2007

1/2x2/3x3/4x................. x 2006/2007= ( rút gọn tử số với mẫu số ở phân số sau )

= 1/2007

1/2007

(1-1/2x1/2)x(1-1/3x1/3)x(1-1/4x1/4)x…x(1-1/2007x1/2007)
= ( 1 - 1/4 ) x ( 1 - 1/9 ) x ( 1- 1/16) x .....x ( 1 - 1/4028049)
= 3/4 x 8/9 x 15/16 x .....x 4028048 / 4028049
= 3 x 8 x 15 x .....x 4028048 / 4 x 9 x 16 x ......x 4028049
= 1 x 3 x 2 x 4 x 3 x 5 x .....x 2006 x 2008 / 2x2 x 3 x3 x 4 x 4 x .....x 2007 x 2007
= ( 1 x 2 x 3 x .....x 2006) x ( 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)
= 2008 / 2007 x 2
= 1004 / 2007