Question: Let {n1, n2, . . .} denote the collection of natural numbers that do not use the digit 6 in their decimal expansion. Show that

Let {n1, n2, . . .} denote the collection of natural numbers that do not use the digit 6 in their decimal expansion. Show that ∑1/nk converges to a number less than 80. If {m1, m2, . . .} is the collection of numbers that end in 6, then ∑1/mk diverges. If {p1, p2, . . . } is the collection of numbers that do not end in 6, then ∑1/pk diverges.

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