If S is the sum of the reciprocals of the consecutive integers from 91 to 100, inclusive, which of the following is less than S?
I. 1/11
II. 1/10
III. 1/10
Choose the correct choice from the following:  A) II only  B) I only  C) III only  D) II and III only  E) I, II, and III
Since we summarize the reciprocals from 100 to 91, we can say also that we add ten numbers who are all (with one exception 1/100) greater than 1/100, so that the sum must be greater than 1/10.   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.   We can conclude that the sum has to be less than 1/9 but more than 1/10. That leaves us II only a as the only possible answer.
<result>A</result>
If S is the sum of the reciprocals of the consecutive integers from 91 to 100, inclusive, which of the following is less than S?
I. 1/11
II. 1/10
III. 1/10