Đáp án:
Giải thích các bước giải:
`1/41+1/42+1/43+...+1/80`
`=(1/41+1/42+...+1/60)+(1/61+1/62+...+1/80)`
`=>1/41>1/60;1/42>1/60;...;1/59>1/60`
`=>1/41+1/42+...+1/60>1/60+1/60+...+1/60` (Có `20` số hạng).
`=>1/41+1/42+...+1/60>1/3(1)`
`=>1/61>1/80;1/62>1/80;...;1/79>1/80`
`=>1/61+1/62+...+1/80>1/80+1/80+...+1/80` (Có `20` số hạng).
`=>1/61+1/62+...+1/80>1/4(2)`
Từ `(1)` và `(2)` ta có:
`=>1/41+1/42+1/43+...+1/80>1/3+1/4`
`=>1/41+1/42+1/43+...+1/80>7/12`
Vậy `1/41+1/42+1/43+...+1/80>7/12`.
