Đáp án:
Giải thích các bước giải:
`=>P=1/(1.2.3)+1/(2.3.4)+1/(3.4.5)+...+1/(2017.2018.2019)`
`=>2P=2/(1.2.3)+2/(2.3.4)+2/(3.4.5)+...+2/(2017.2018.2019)`
`=>2P=1/1.2-1/2.3+1/2.3-1/3.4+1/3.4-1/4.5+...+1/2017.2018-1/2018.2019`
`=>2P=1/2-1/2018.2019`
`=>P=1/4-1/(2.2018.2019`
Vậy `P=1/4-1/(2.2018.2019`
`=>P=1/(1.2.3)+1/(2.3.4)+1/(3.4.5)+...+1/(2014.2015.2016`
`=>2P=2/(1.2.3)+2/(2.3.4)+2/(3.4.5)+...+2/(2014.2015.2016`
`=>2P=1/1.2-1/2.3+1/2.3-1/3.4+1/3.4-1/4.5+...+1/2014.2015-1/2015.2016`
`=>2P=1/1.2-1/2015.2016`
`=>P=1/4-1/(2.2015.2016)<1`
`=>P<1`
Vậy `P<1`.