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- #1

{

*f*

_{0}=0;

*f*

_{1}= 1 and

{

*f*

_{n}=

*f*

_{n}- 1 +

*f*

_{n}-2 for n 2

Prove by generalized mathematical induction that

*f*

_{n}= 1/sqrt(5)[ϕ

^{n}- (-ϕ)

^{-n}]

where ϕ = [1+sqrt(5)]/2

is the

*golden ratio.*. (This is known as de Moivre's formula.)

So I'm completely lost as to how I should start this and I need someone to point me in the right direction. Thanks.