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
What I found by Hugo)
Given this sequence sums to 10/89ths. 9*10/89= 1+ 1/89
<-- a power of ten off plus 1. 99*10/89 = 990/89 or 11 and
11/89ths. The decimal portion of which is 10/89 +
1/89th. What I assume is confusing people is why the two numbers
look so alike. Answer is that it is the fibonacci sequence.
0 1 1 2 3 5
+ 0 1 1 2 3
= 0 1 2 3 5 8
The method it builds is part of the genious behind the sequience.
-Douglas
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Posted by Douglas
on 2005-03-31 08:00:52 |
re: What I found
