Hãy c/m rằng: `T=1/2 + 1/3 + 1/4 + ... + 1/16 + 1/17` không phải là số tự nhiên

`\text{Giải}` `\text{thích}` `\text{các}` `\text{bước}` `\text{giải}:`

`\text{T` `= 1/2 +1/3+1/4+...+1/16+1/17`

`\text{T` `=` `(1/2 + 1/3 + 1/4 + 1/5)` `+` `(1/6 + 1/7 + 1/8)` `+`

`(1/9 + 1/10 + 1/11)` `+` `(1/12 + 1/13 + 1/14)` `+`

`(1/15 + 1/16 + 1/17)`

`\text{T` `<(1/2 + 1/3 + 1/4 + 1/5) + 3(1/6) + 3(1/9) + 3(1/12) + 3(1/15) = 2(1/2 + 1/3 + 1/4 + 1/5)`

`\text{T` `< 2(1/2 + 1/2 + 1/4 + 1/4) = 3`

`\text{Mặt` `\text{khác:`
`\text{T` `=` `(1/2 + 1/3 + 1/4)` `+` `(1/5 + 1/6 + 1/7 + 1/8)` `+`

`(1/9 + 1/10 + 1/11 + 1/12)` `+` `(1/13 + 1/14 + 1/15 + 1/16)` `+` `1/17`

`\text{T` `>(1/2 + 1/3 + 1/4) + 4(1/8) + 4(1/12) + 4(1/16) = 2(1/2 + 1/3 + 1/4)`

`\text{T` `>2(1/2 + 1/4 + 1/4) = 2`     

`=>  2 <` `\text{T` `< 3`
`\text{Vậy` `\text{T` `\text{không}` `\text{phải}` `\text{là}` `\text{số}` `\text{tự}` `\text{nhiên`.