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)?

(In reply to No Subject by Dustin)

I haven't been able to come up with any worthwhile connection to e, pi, or the golden ratio.  However, if you substitute sqrt(1.5) in place of sqrt(5) in the golden ratio, it's pretty close: 0.112372436, as opposed to 0.112359551.

Posted by Dustin on 2005-03-09 19:14:58