M is the sum of the reciprocals of the consecutive integers from 601 to 700, inclusive. Which of the following is true? Answers.
A) 1/7 < M < 1/6
B) 1/5 < M < 1/3
C) 1/7 < M < 1/5
D) 1/9 < M < 1/7
E) 1/12 < M < 1/9
M = 1/601 + 1/602 + 1/603 + ...... + 1/700   If we replace the first 99 terms by 1/700, then we get a sum = 100/700 = 1/7. Since the actual terms are larger than 1/700, the sum is larger than 1/7.   If we replace the all the 100 terms by 1/600, we get a sum = 100/600 = 1/6. Since the actual terms are smaller than 1/600, the sum is less than 1/6.   Therefore 1/7 &lt; M &lt; 1/6   Choice 1/7 &lt; M &lt; 1/6
<result>A</result>
M is the sum of the reciprocals of the consecutive integers from 601 to 700, inclusive. Which of the following is true?