"89" and the Fibonacci Series
The reciprocal of 89, a Fibonacci number, is based on the
Fibonacci series
This is a little curiousity involving the number 89, the twelfth number in
the Fibonacci series.
If you take each Fibonacci number, divide it by 10 raised to the power of
its position in the Fibonacci sequence and add them all together, you get 0.011235955...,
the same number as the reciprocal of 89.
Note: You can see the beginning of the Fibonacci sequence in the first 6
digits of the decimal equivalent of 1/89. (i.e., 0,1,1,2,3,5 appears as 0.011235..)
Note the Fibonacci series in green
Note the sequence number of the Fibonacci series in red |
1 / 89 =
0 / (10 ^ 1 ) +
1 / (10 ^ 2 ) +
1 / (10 ^ 3 ) +
2 / (10 ^ 4 ) +
3 / (10 ^ 5 ) +
5 / (10 ^ 6 ) +
8 / (10 ^ 7 ) +
13 / (10 ^ 8 ) +
. . . |
0.011235955
=
0.0 +
0.01 +
0.001 +
0.0002 +
0.00003 +
0.000005 +
0.0000008 +
0.00000013 +
. . . |
|
