Hi!
This question is testing your ability to find limits and estimate.
We're told that K is the sum of the reciprocals of the integers 43 through 48, inclusive. In other words:
K = 1/43 + 1/44 + 1/45 + 1/46 + 1/47 + 1/48
well, that's a whole mess of ugly math, so there's got to be a way to answer the question without actually calculating.
The quickest way to do so is to think of 2 extreme ranges and then know the answer has to be in the middle.
If we were summing 1/48 + 1/48 + 1/48 + 1/48 + 1/48 + 1/48, then the answer would be 6/48 = 1/8.
So, we know the answer has to be more than 1/8, since 5 of our numbers are bigger than the ones used in the estimate.
If we were summing 1/42 + 1/42 + 1/42 + 1/42 + 1/42 + 1/42, then the answer would be 6/42 = 1/7.
So, we know the answer has to be less than 1/7, since all 6 of our numbers are smaller than the ones used in the estimate.
Therefore, 1/8 < K < 1/7
Since 1/7 isn't there (and it would never be in the answers for this question, since you'd have to do the math to be 100% sure whether K were closer to 1/7 or 1/8), of the choices provided K is definitely closest to 1/8... choose (C)!
