perplexus.info :: Just Math : Fibonacci Fractions

Fibonacci Fractions (Posted on 2005-03-09)

What is the sum of 0.1+ 0.01+ 0.002+ 0.0003+ 0.00005+ 0.000008+ ..., where each term is the n-th Fibonacci number, shifted n places to the right (that is, divided by 10^n)?

See The Solution Submitted by e.g.

Rating: 3.0000 (2 votes)

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maybe

| Comment 4 of 17 |

I got 1/(Phi*5.5) where Phi=(5^^.5+1)/2 = 1.618...

I was never good at proofs but this might be a start:

Óphi^^n/(5^^.5*10^^n)=

Posted by Mark on 2005-03-09 19:56:43

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