If S is the sum of the reciprocals of the consecutive integers from 41 to 50, inclusive, which of the following is less than S?
I. 1/4
II. 1/5
III. 1/6
IV. 1/4>S >1/5
Pick:  A) I  B) II  C) III  D) I&II  E) IV
Since we summarize the reciprocals from 50 to 41, we can say also that we add ten numbers who are all (with one exception 1/50) greater than 1/50, so that the sum must be greater than 1/5.   On the other side we can say that we add the reciprocals from 41 to 50, so that the sum has to be less than the sum of ten times 1/41.   sum has to be greater than 1/5 and less than 1/4   IV
<result>E</result>
If S is the sum of the reciprocals of the consecutive integers from 41 to 50, inclusive, which of the following is less than S?
I. 1/4
II. 1/5
III. 1/6
IV. 1/4>S >1/5