Let r1, r2, . . . , rn, . . . be an enumeration of the rational

Question:

Let r1, r2, . . . , rn, . . . be an enumeration of the rational numbers in the interval [0,1]. (See Section 1.3.) For a given e > 0, put an interval of length en about the nth rational number rn for n = 1, 2, 3, . . . , and find the total sum of the lengths of all the intervals. Evaluate this number for ε = 0.1 and ε = 0.01.