If \(a\) is the sum of the reciprocals of the consecutive integers from \(11\) to \(20,\) and \(b\) is the estimated sum

If \(a\) is the sum of the reciprocals of the consecutive integers from \(11\) to \(20,\) and \(b\) is the estimated sum of the same numbers, so each even integer is rounded up to the nearest \(10\) and each odd integer is rounded down to the nearest \(10,\) then \(a - b\) is between:

A. \(-\dfrac14\) and \(\dfrac14\)

B. \(\dfrac14\) and \(\dfrac34\)

C. \(\dfrac34\) and \(\dfrac54\)

D. \(\dfrac54\) and \(\dfrac32\)

E. \(\dfrac74\) and \(\dfrac{11}2\)

Answer: A

Source: Economist