M is the sum of the reciprocals of the consecutive integers from 401 to 500, inclusive. Which of the following is true?
Choices
A) 1/3 < M < 1/2	B) 1/5 < M < 1/4	C) 1/7 < M < 1/5	D) 1/9 < M < 1/7	E) 1/12 < M < 1/9
M = 1/401 + 1/4+ 1/403 + ...... + 1/500   If we replace the first 99 terms by 1/500, then we get a sum = 100/500 = 1/5. Since the actual terms are larger than 1/500, the sum is larger than 1/5.   If we replace the all the 100 terms by 1/400, we get a sum = 100/400 = 1/4. Since the actual terms are smaller than 1/400, the sum is less than 1/4.   Therefore 1/5 &lt; M &lt; 1/4   Choice 1/5 &lt; M &lt; 1/4
<result>B</result>
M is the sum of the reciprocals of the consecutive integers from 401 to 500, inclusive. Which of the following is true?