M is the sum of the reciprocals of the consecutive integers from 501 to 600, inclusive. Which of the following is true?	Answers.
A) 1/3 < M < 1/2 B) 1/5 < M < 1/3 C) 1/7 < M < 1/5 D) 1/6 < M < 1/6 E) 1/12 < M < 1/9
M = 1/501 + 1/502 + 1/503 + ...... + 1/600   If we replace the first 99 terms by 1/600, then we get a sum = 100/600 = 1/6. Since the actual terms are larger than 1/600, the sum is larger than 1/6.   If we replace the all the 100 terms by 1/500, we get a sum = 100/500 = 1/5. Since the actual terms are smaller than 1/500, the sum is less than 1/5.   Therefore 1/6 &lt; M &lt; 1/5   Choice 1/6 &lt; M &lt; 1/6
<result>D</result>
M is the sum of the reciprocals of the consecutive integers from 501 to 600, inclusive. Which of the following is true?