M is the sum of the reciprocals of the consecutive integers from 101 to 200, inclusive. Which of the following is true?	Choose one.
A) 1/3 < M < 1/2  B) 1/5 < M < 1/3  C) 1/2 < M < 1  D) 1/9 < M < 1/7  E) 1/12 < M < 1/9
M = 1/101 + 1/102 + 1/103 + ...... + 1/200   If we replace the first 99 terms by 1/200, then we get a sum = 100/200 = 1/2. Since the actual terms are larger than 1/200, the sum is larger than 1/2.   If we replace the all the 100 terms by 1/100, we get a sum = 100/100= 
<gadget id="calculator">100/100</gadget>
<output>1</output>
1. Since the actual terms are smaller than 1/100, the sum is less than 1.   Therefore 1/2 &lt; M &lt; 1   1/2 &lt; M &lt; 1hoice 1/2 &lt; M &lt; 1
<result>C</result>
M is the sum of the reciprocals of the consecutive integers from 101 to 200, inclusive. Which of the following is true?