Đáp án: `1/2+2/3+3/4+...+2019/2020>5`
Giải thích các bước giải:
`1/2+2/3+3/4+...+2019/2020`
`=(2-1)/2+(3-1)/3+(4-1)/4+...+(2020-2019)/2020`
`=1-1/2+1-1/3+1-1/4+...+1-1/2020`
`=(1+1+1+...+1)-(1/2+1/3+1/4+...+1/2020)`
`=2019-(1/2+1/3+1/4+...+1/2020)`
Ta có:
`1/2 + 1/3 + ... + 1/2020 < 1/2 + 1/2 + 1/2 + ... + 1/2 = 1/2. 2019 = 2019/2 = 1009,5`
`⇒ - (1/2 + 1/3 + ... + 1/2020) > - 1009,5`
`⇒2019 - (1/2 + 1/3 + ... + 1/2020) > 2019 - 1009,5 = 1009,5 > 5`
`⇒ A>5`
Vậy `A>5`.
