Toán ( 1-1/10)x(1-1/11)x(1-1/12)x…x(1-1/2003) 26/07/2021 By Brielle ( 1-1/10)x(1-1/11)x(1-1/12)x…x(1-1/2003)
(1- $\frac{1}{10}$ )×(1- $\frac{1}{11}$ )×(1- $\frac{1}{12}$ )×…×(1- $\frac{1}{2003}$ ) = ( $\frac{10}{10}$ – $\frac{1}{10}$ )×( $\frac{11}{11}$ – $\frac{1}{11}$ )×( $\frac{12}{12}$ – $\frac{1}{12}$ )×…×( $\frac{2003}{2003}$ – $\frac{1}{2003}$ ) = $\frac{9}{10}$ × $\frac{10}{11}$ × $\frac{11}{12}$ × … × $\frac{2002}{2003}$ = $\frac{9}{2003}$ Trả lời
`( 1 – 1/10 ) . ( 1 – 1/11 ) . ( 1 – 1/12 ) ….. ( 1 – 1/2003 )` `= 9/10 . 10/11 . 11/12 ….. 2002/2003` `= ( 9 . 10 . 11 …. 2002 )/( 10 . 11 . 12 …. 2003 )` `= 9/2003` Trả lời
(1- $\frac{1}{10}$ )×(1- $\frac{1}{11}$ )×(1- $\frac{1}{12}$ )×…×(1- $\frac{1}{2003}$ )
= ( $\frac{10}{10}$ – $\frac{1}{10}$ )×( $\frac{11}{11}$ – $\frac{1}{11}$ )×( $\frac{12}{12}$ – $\frac{1}{12}$ )×…×( $\frac{2003}{2003}$ – $\frac{1}{2003}$ )
= $\frac{9}{10}$ × $\frac{10}{11}$ × $\frac{11}{12}$ × … × $\frac{2002}{2003}$
= $\frac{9}{2003}$
`( 1 – 1/10 ) . ( 1 – 1/11 ) . ( 1 – 1/12 ) ….. ( 1 – 1/2003 )`
`= 9/10 . 10/11 . 11/12 ….. 2002/2003`
`= ( 9 . 10 . 11 …. 2002 )/( 10 . 11 . 12 …. 2003 )`
`= 9/2003`