Problem Solving

Bhupisuhag wrote:If K is the sum of the reciprocals of the consecutive integers from 43 to 48, inclusive, then K is
closest in value to which of the following ?

1) 1/12
2) 1/10
3) 1/8
4) 1/6
5) 1/4

We want the approximate sum of 1/43 + 1/44 + 1/45 + . . . + 1/48

Let's make the following observations about the upper and lower bounds:
Upper bounds: If all 6 fractions were 1/43, the sum would be (6)(1/43) = 6/43 ~ 6/42 = 1/7
Lower bounds: If all 6 fractions were 1/48, the sum would be (6)(1/48) = 6/48 = 1/8

From this we can conclude that 1/8 < K < 1/7

If K is between 1/8 and 1/7, then K must be closer to 1/8 than it is to 1/6

Answer = C

Cheers,
Brent