0.01 + 0.001 + 0.0002 + 0.00003 + 0.000005 + 0.0000008... = 1/89
The fibonacci sequence shows up in surprising places.
1/89 =
0.01 +
0.001 +
0.0002 +
0.00003 +
0.000005 +
0.0000008 +
0.00000013 +
0.000000021 +
0.0000000034...
Found this in "Numbers are Forever - Mathematical Facts and Curios".
