Đặt A =$\dfrac{1}{1.4}$ + $\dfrac{1}{4.7}$ + .... + $\dfrac{1}{100.103}$
`=> 3A =` 3 . ( $\dfrac{1}{1.4}$ + $\dfrac{1}{4.7}$ + .... + $\dfrac{1}{100.103}$ )
`=> 3A =` $\dfrac{3}{1.4}$ + $\dfrac{3}{4.7}$ + .... + $\dfrac{3}{100.103}$
`=> 3A =` `1/1` - `1/4` + .... + $\dfrac{1}{100}$ - $\dfrac{1}{103}$
`=> 3A =` `1/1` - $\dfrac{1}{103}$
`=> 3A =` $\dfrac{102}{103}$
`=> A =` $\dfrac{102}{103}$ `: 3`
`=> A =` $\dfrac{34}{103}$
