A few years back, I thought of this method as a way of
representing a numbers inverse as an infinite summation. I doubt
its original, so Let me describe it and maybe you can tell me if you've seen this before.

VB Code:
  1. Given a Base number, and a Number to get its inverted infinite expansion based on the base number,

  2.  
  3. Start with 6 columns:

  4.  
  5. Col1    Col2a   Col3    Col4    Col5    Col2b

  6.  
  7. Where:

  8. Col1 = Line #, Initial condition = 0

  9. Col3 = Number to convert

  10. Col4 = Number of times Col3 value can be subtracted from Col2a or Col2b

  11. Col2a and Col2b : Alternate between Base * (Value of Col2a or Col2b of last line), empty, or

  12.  col2a = col2b - col3*col4, or col2b = col2a – col3*col4

  13. Col5 : Inverse sequence of Col1, Built when:

  14. value of Col2a or Col2b previously in Col2a or Col2b. Ignored when Col2a or Col2b ends at 0.

ok. I don't want to turn this into a midterm essay, so I'll go strait to an example.
Lets say you wanted to express 1/11 as an infinete summation of 2^(-n1) + 2^(-n2) + 2^(-n3) + ...
{2 is the base}
The Col’s initial conditions are:
0, 1, 11, 0, Blank, Blank.
Watch This:


The reason I put the 1* in is if you were using a different base, ie 3, 5, etc… you can have a number from 1 to (Base – 1) as a Multiplier.

Has anybody seen this Or something similar before?

-Lou