`#Kenshiro`
`S = 1/(1!) + 1/(2!) + 1/(3!) + ... + 1/(2019!) < 3`
Ta có :
`1/(2!) = 1/1.2`
`1/(3!) = 1/2.3`
`1/(2019!) = 1/2019.2020`
`⇔ 1/1.2 + 1/2.3 + ... + 1/2019.2020`
`⇔ 1 - 1/2 + 1/2 - 1/3 + ... + 1/2019 - 1/2020`
`⇔ 1 - 1/2020 = 2019/2020`
`⇒ 1 + 1/(1!) + 1/(2!) + 1/(3!) + ... + 1/2020 < 1 ⇔ 1 + 1/(1!) + 1/(2!) + 1/(3!) + ... + 1/2019 < 3`
`⇒ S < 3`