If S is the sum of the reciprocals of the consecutive integers from 81 to 90, inclusive, which of the following is less than S?
I. 1/8
II. 1/9
III. 1/10
IV. 1/5
V. 1/8>S >1/9
Pick one
A) V B) I C) II D) III E) IV
Since we summarize the reciprocals from 90 to 81, we can say also that we add ten numbers who are all (with one exception 1/90) greater than 1/90, so that the sum must be greater than 1/9.   On the other side we can say that we add the reciprocals from 91 to 100, so that the sum has to be less than the sum of ten times 1/91.   sum has to be greater than 1/9 and less than 1/8   V
<result>A</result>
If S is the sum of the reciprocals of the consecutive integers from 81 to 90, inclusive, which of the following is less than S?
I. 1/8
II. 1/9
III. 1/10
IV. 1/5
V. 1/8>S >1/9