I just put up a blog post covering this and a number of other interesting decimal expansions:

fibonacci: 100000000/99989999=1.000100020003000500080013002100340055...

integers: 1000000/998001=1.002003004005006...

square numbers: 1001000000/997002999=1.004009016025036...

explanations and proofs at: http://www.joefkelley.com/?p=635