Ta có :

`S=1/2+1/3+1/4+1/5+1/6+1/7+1/8`

`=>S=1/2+(1/3+1/4+1/5+1/6+1/7+1/8)>1/2+(1/8+1/8+1/8+1/8+1/8+1/8)`

`=1/2+1/8 .6 `

`=1/2+6/8`

`=1/2+3/4`

`=2/4+3/4=5/4` 

`=>S>1` `` `` `` `` `` ``$(1)$

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`S=1/2+1/3+1/4+1/5+1/6+1/7+1/8`

`=>S=1/2+1/3+(1/4+1/5+1/6+1/7)+1/8<1/2+1/3+(1/4+1/4+1/4+1/4)+1/8`

`=1/2+1/3+1/4 .4 +1/8`

`=12/24+8/24+1+3/24`

`=(12/24+8/24+3/24)+1`

`=23/24+1=47/24`

`=>S<2` `` `` `` `` `` ``$(2)$

Từ $(1)$ và $(2)$ `=>1<S<2`

`=>S` không là số tự nhiên

Vậy `S` không là số tự nhiên

 

Đáp án:

 

Giải thích các bước giải:

`***S = 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8`

`S = 1/2 + (1/3+1/4+1/5+1/6+1/7+1/8)`

`S > 1/2+ (1/8+1/8+1/8+1/8+1/8+1/8)`

`S > 1/2 + 3/4`

`S > 5/4 > 1`

`*** S =1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8`

     `S = 1/2+(1/3+1/4+1/5) + (1/6+1/7+1/8)`

     `S < 1/2 + (1/3+1/3+1/3) + (1/6+1/6+1/6)`

     `S < 1/2 + 1 + 1/2`

     `S < 2`

`=> 1<S < 2 => S` không phải là số tự nhiên