Azizakaria wrote:M is the sum of 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
If all of the 100 values were 1/300, the result would be the following sum:
100(1/300) = 1/3.
Since all but one of the values are actually GREATER THAN 1/300, the value of M must be GREATER THAN 1/3.
If all of the 100 values were 1/200, the result would be the following sum:
100(1/200) = 1/2.
Since all of the values are actually LESS THAN 1/200, the value of M must be LESS THAN 1/2.
Thus:
1/3 < M < 1/2.
The correct answer is
A.
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