Đáp án:
`S>5/4`
Giải thích các bước giải:
`S=1/21+1/22+1/23+...+1/149+1/150`
`=>S=(1/21+1/22+...+1/40)+(1/41+1/42+...+1/80)+...+1/150`
Ta thấy `1/21>1/40;1/22>1/40;...;1/39>1/40`
`=>1/21+1/22+...+1/40>1/40+1/40+...+1/40` (Có `20` số hạng)
`=>1/21+1/22+...+1/40>1/2(1)`
Ta thấy `1/41>1/80;1/42>1/80;...;1/79>1/80`
`=>1/41+1/42+...+1/80>1/80+1/80+...+1/80` (Có `40` số hạng)
`=>1/41+1/42+...+1/2(2)`
Ta thấy `1/81>1/150;1/82>1/150;...;1/149>1/150`
`=>1/81+1/82+...+1/150>1/150+1/150+...+1/150` (Có `70` số hạng)
`=>1/81+1/82+...+1/150>7/15(3)`
Từ `(1),(2)` và `(3)` ta có:
`=>1/21+1/22+1/23+...+1/149+1/150>1/2+1/2+7/15`
`=>1/21+1/22+1/23+...+1/149+1/150>1+7/15`
`=>1/21+1/22+1/23+...+1/149+1/150>22/15>5/4`
`=>1/21+1/22+1/23+...+1/149+1/150>5/4`
Vậy `S>5/4`.
