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)?

Using Excel (which is known for its impreciseness when it comes to big numbers):

n  sum

1  0.1
2  0.11
3  0.112
4  0.1123
5  0.11235
6  0.112358
7  0.1123593
8  0.11235951
9  0.112359544
10 0.11235955
11 0.11235955
12 0.112359551
13 0.112359551
14 0.112359551

From 12 all the way to 308, it says 0.112359551.  Apparently, Excel can't perform 10^309.

I'm not sure what 0.112359551 represents.

Edited on March 9, 2005, 6:54 pm

Posted by Dustin on 2005-03-09 18:52:04