`A=` `\frac{4}{1.2}+` `\frac{4}{2.3}+` `\frac{4}{3.4}+...+` `\frac{4}{2014.2015}`
`⇒` `A=` `4.(\frac{1}{1.2}+` `\frac{1}{2.3}+` `\frac{1}{3.4}+...+` `\frac{1}{2014.2015})`
`⇒``A=` `4.(\frac{1}{1}-``\frac{1}{2}+``\frac{1}{2}-``\frac{1}{3}+``\frac{1}{3}``-``\frac{1}{4}``+``...+``\frac{1}{2014}``-``\frac{1}{2015})`
`⇒` `A=` `4.(\frac{1}{1}-``\frac{1}{2015})`
`⇒` `A=` `4.` `\frac{2014}{2015}`
`⇒` `A=` `\frac{8056}{2015}`
Vậy : `A=` `\frac{8056}{2015}`
