[seqfan] Question about A003592.

[L. Edson Jeffery]

A003592 = {numbers of the form 2^i*5^j, with i, j >= 0} = {1, 2, 4, 5, 8,
10, 16, 20, 25, 32, 40, 50, 64, 80, 100, ...}.

In A003592 David Wasserman states that each 1/A003592(n) has terminating
decimal expansion. He gave no references, so I assume that he has worked
out a proof. Then it follows that

(1) sum_{k=1..n} 1/A003592(k)

is terminating. The partial sums (1) seem to be converging, so I wonder:
can someone compute the limit as n -> infinity?

Ed Jeffery