`1/5 + 1/6 + 1/7 + ... + 1/17`
` = (1/5 + 1/6+1/7 +1/8 +1/9)+(1/10 +1/11+1/12 + ...+1/17)`
Ta thấy :
`1/5 =1/5`
`1/6 < 1/5`
`1/7 < 1/5`
`1/8 <1/5`
`1/9 <1/5`
`=> 1/5 + 1/6+1/7 +1/8 +1/9 < 1/5 + 1/5 + 1/5 + 1/5 + 1/5`
`=> 1/5 + 1/6+1/7 +1/8 +1/9 < 1/5 . 5 = 1`
Ta thấy :
`1/10 = 1/10`
`1/11 < 1/10`
`1/12 <1/10`
`....`
`1/17 <1/10`
`=>1/10 +1/11+1/12 + ...+1/17 < 1/10 +1/10 +..+1/10`
`=> 1/10 +1/11+1/12 + ...+1/17 < 1/10 . 8 = 4/5`
`=> 1/5 + 1/6+1/7 +1/8 +1/9+1/10 +1/11+1/12 + ...+1/17 < 1 +4/5`
`=> 1/5 + 1/6+1/7 +1/8 +1/9+1/10 +1/11+1/12 + ...+1/17 < 9/5`
`=> 1/5 + 1/6+1/7 +1/8 +1/9+1/10 +1/11+1/12 + ...+1/17 < 10/5 ( do\ 9/5 < 10/5)`
`=> 1/5 + 1/6+1/7 +1/8 +1/9+1/10 +1/11+1/12 + ...+1/17 < 2`
