If S is the sum of the reciprocals of the consecutive integers from 71 to 80, inclusive, which of the following is less than S?
I. 1/7
II. 1/8
III. 1/9
IV. 1/7>S >1/8  Choose one.
A) I  B) IV  C) II  D) III  E) I&II
Since we summarize the reciprocals from 80 to 71, we can say also that we add ten numbers who are all (with one exception 1/80) greater than 1/80, so that the sum must be greater than 1/8.   On the other side we can say that we add the reciprocals from 71 to 80, so that the sum has to be less than the sum of ten times 1/81.   sum has to be greater than 1/8 and less than 1/7   IV
<result>B</result>
If S is the sum of the reciprocals of the consecutive integers from 71 to 80, inclusive, which of the following is less than S?
I. 1/7
II. 1/8
III. 1/9
IV. 1/7>S >1/8