On the Phis Fascinating Figures page the Things To Do in the Numerical Relationships between Phi and its Powers section asked you to investigate what happens when instead of subtracting the powers of Phi and phi as in the formula for Fibn above we added t

n:

Phin

(-phi)n

Phin+(-phi)n

0

1 000000000

1 000000000

2 000000000

1

1618033989

-0618033989

1 000000000

2

2618033989

0318196601

3000000000

3

4236067978

-0236067978

4000000000

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