A=102/101! - 103/102! +...+2018/2017! -2019/2018!
Ta có
102/101!=101/101! + 1/101!=1/100! + 1/101!
103/102!=102/102! + 1/102!=1/101! + 1/102!
...
2019/2018!=1/2017! + 1/2018!
⇒A=1/100! + 1/101! -1/101! - 1/102! +...+1/2016! + 1/2017! - 1/2017! -1/2018!
=1/100! - 1/2018!
⇒A<1/100!