M is the sum of the reciprocals of the consecutive integers from 201 to 300, inclusive. Which of the following is true?
(A) 1/3 < m < 1/2
(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 = 1/201 + 1/202 +...+ 1/300.
If all of the 100 terms in the sum were 1/300, the result would be the following sum:
100(1/300) = 1/3.
If all of the 100 terms in the sum were 1/200, the result would be the following sum:
100(1/200) = 1/2.
Since all of the terms in the sum are BETWEEN 1/300 and 1/200, the sum must be BETWEEN 1/3 and 1/2.
The correct answer is
A.
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