Correct? "phi - (((1 / phi) * (1 - ((1 / phi)^70))) / (1 - (1 / phi))) = 0"

phi - (((1 / phi) * (1 - ((1 / phi)^70))) / (1 - (1 / phi))) = 0 is not verified by what I figure out with my Excel Trigonometry.


06/12/12

((1 / phi) * (1 - ((1 / phi)^70))) / (1 - (1 / phi)) = 1.61803399, more precisely, means that:

1. 1/phi + 1/phi^2 + 1/phi^3 + .... + 1/phi^70 is 1.618033988..
   


2. 1/phi + 1/phi^2 + 1/phi^3 + .... + 1/phi^70 + .... + 1/phi^n
   becomes indefinately closer to phi as 'n' increases to infinity.
   
   Phi to 20,000 places

Note:

1. 1/phi, 1/phi^2, 1/phi^3, ... forms Fibonacci Numbers


2. Formula for the geometrical series for this:
   (((1 / phi) * (1 - ((1 / phi)^n))) / (1 - (1 / phi)))


3. phi+1, (phi+1)^2, (phi+1)^3, ... also forms Fibonacci Numbers