K = 1/43 + 1/44 + 1/45 + 1/46 + 1/47 + 1/48.If K is the sum of reciprocals of the consecutive integers from 43 to 48, inclusive, then K is closest in value to which of the following?
A. 1/12
B. 1/10
C. 1/8
D. 1/6
E. 1/4
Determine the RANGE of the sum.
The smallest fraction = 1/48.
If all of the 6 fractions were 1/48, the result would be the following sum:
6(1/48) = 1/8.
Since all but one of the fractions are actually GREATER THAN 1/48, the value of K must be GREATER THAN 1/8.
The greatest fraction = 1/43.
If all of the 6 fractions were 1/42, the result would be the following sum:
6(1/42) = 1/7.
Since all of the fractions are actually LESS THAN 1/42, the value of K must be LESS THAN 1/7.
Thus:
1/8 < K < 1/7.
Answer choices A and B are BELOW this range.
Answer choices D and E are ABOVE this range.
The correct answer is C.
