Đáp án:
`⇒S=\frac{1018585}{4074342}`
Giải thích các bước giải:
`S=\frac{1}{1.2.3}+\frac{1}{2.3.4}+....+\frac{1}{2017.2018.2019}`
`⇒S=\frac{1}{2}.(\frac{2}{1.2.3}+\frac{2}{2.3.4}+....+\frac{2}{2017.2018.2019})`
`⇒S=\frac{1}{2}.(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+....+\frac{1}{2017.2018}-\frac{1}{2018.2019})`
`⇒S=\frac{1}{2}.(\frac{1}{2}-\frac{1}{4074342})`
`⇒S=\frac{1018585}{4074342}`