Bài `8 :`
`A = 9/( 1 . 2 ) + 9/( 2 . 3 ) + 9/( 3 . 4 ) + .... + 9/( 98 . 99 ) + 9/( 99 . 100 )`
`A = 9 . ( 1/( 1 . 2 ) + 1/( 2 . 3 ) + 1/( 3 . 4 ) + .... + 1/( 98 . 99 ) + 1/( 99 . 100 ) )`
`A = 9 . ( 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + .... + 1/98 - 1/99 + 1/99 - 1/100 )`
`A = 9 . ( 1 - 1/100 )`
`A = 9 . 99/100`
`A = 891/100`
Bài `2 :`
`a, ( 3 1/2 + 2x ) . 2 2/3 = 5 1/3`
`⇔ ( 7/2 + 2x ) . 8/3 = 16/3`
`⇔ 7/2 + 2x = 16/3 : 8/3`
`⇔ 7/2 + 2x = 2`
`⇔ 2x = 2 - 7/2`
`⇔ 2x = ( - 3 )/2`
`⇔ x = ( - 3 )/2 : 2`
`⇔ x = ( - 3 )/4`
Vậy `, x = ( - 3 )/4 .`
`b, | 2x + 3 | = 5`
`⇔` \(\left[ \begin{array}{l}2x + 3 = 5\\2x + 3 = - 5\end{array} \right.\)
`⇔` \(\left[ \begin{array}{l}2x = 2\\2x = - 8\end{array} \right.\)
`⇔` \(\left[ \begin{array}{l}x = 1\\x = - 4\end{array} \right.\)
Vậy `, x ∈ { 1 ; - 4 } .`
`c, ( x - 2 )/4 = ( 5 + x )/3`
`⇔ ( x - 2 ) . 3 = ( 5 + x ) . 4`
`⇔ 3x - 6 = 20 + 4x`
`⇔ 3x - 4x = 20 + 6`
`⇔ - x = 26`
`⇔ x = - 26`
Vậy `, x = - 26 .`