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Fibonacci sequence in closed form

Prove that Fn can be expressed by:
Fn=[(a^n-b^n)/(a-b)] for n=1,2,3...

~: Set Gn=[(a^n-b^n)/(a-b)] and show that Gn satisfies the recurrence formula {G(n+1) = Gn + G(n-1) for n=2,3,4...} and don't forget that a and b satisfy the equation x^2-x-1=0.
a and b are the roots of x^2-x-1=0, which are (1+sqrt5)/2 and (1-sqrt5)/2.