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)?

With a little trick, my Excel goes to 10^68, giving as sum:
0.112359550561798
I (also) have no idea what this is, but if you multiply it with 9 then you get
1.01123595505618
multiplying with 99 gives
11.23595505618
The 8 at the end is probably some rounding of 798.
It seems to shift the 112359... digits, but I don't see how this works

Posted by Hugo on 2005-03-09 19:44:51