If S is the sum of the reciprocals of the consecutive integers from 51 to 60, inclusive, which of the following is less than S?
I. 1/5
II. 1/6
III. 1/7
IV. 1/5>S >1/6 Choose the correct choice from the following answers.
A) I B) II C) III D) IV E) I & II
Since we summarize the reciprocals from 60 to 51, we can say also that we add ten numbers who are all (with one exception 1/60) greater than 1/60, so that the sum must be greater than 1/6.   On the other side we can say that we add the reciprocals from 51 to 60, so that the sum has to be less than the sum of ten times 1/51.   sum has to be greater than 1/6 and less than 1/5   IV
<result>D</result>
If S is the sum of the reciprocals of the consecutive integers from 51 to 60, inclusive, which of the following is less than S?
I. 1/5
II. 1/6
III. 1/7
IV. 1/5>S >1/6