Bài 6 (0,5 điểm). Hãy chứng tỏ rằng T = $\frac{1}{2}$ + $\frac{1}{3}$ + $\frac{1}{4}$ +...+ $\frac{1}{16}$ + $\frac{1}{17}$  không phải là số tự nhiên.

Ta có:

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

`=(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)`

`<(1/2+1/3+1/4+1/5)+3 . 1/6 +3.1/9+3. 1/12+ 3 .1/15`

`=(1/2+1/3+1/4+1/5)+1/2+1/3+1/4+1/5`

`=2(1/2+1/3+1/4+1/5)`

`< 2. (1/2 +1/2 +1/4 +1/4)`

`=3`

Lại có:

`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`

`> (1/2+1/3+1/4)+ 4. 1/8+4. 1/12+3. 1/16+0`

`=2(1/2+1/3+1/4)`

`> 2 .(1/2 +1/4+1/4)`

`=2`

`→` `2<T<3`

`→` T không phải là số tự nhiên.