Đáp án:

`S = 1 + 1/2 + 1/3 + 1/4 + ... + 1/63`

`S = 1 + 1/2 + (1/3 + 1/4) + (1/5 + 1/6 + 1/7 + 1/8) + (1/9 + ... + 1/16) + (1/17 + ... + 1/32) + (1/33 + ... + 1/63)`

Ta thấy:

`1/3 + 1/4 > 1/4 + 1/4 = 1/2`

`1/5 + 1/6 + 1/7 + 1/8 > 1/8 + 1/8 + 1/8 + 1/8 = 1/2`

`1/9 + ... + 1/16 > 8 xx 1/16 = 1/2`

`1/17 + ... + 1/32 > 16 xx 1/32 = 1/2`

`1/33 + ... + 1/63 > 31 xx 1/63 > 1/2`

`S > 1 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 = 4 > 3`

Ta lại có: `S = 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + (1/8 + ... + 1/15) + (1/16 + ... + 1/31) + (1/32 + ... + 1/63)`

Ta thấy: 

`1/8 + ... + 1/15 < 8 xx 1/8 = 1`

`1/16 + ... + 1/31 < 16 xx 1/16 = 1`

`1/32 + ... + 1/63 < 32 xx 1/32 = 1`

Suy ra `S < 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1 + 1 + 1`

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

 Vậy `3 < S < 6`