Question: Let {fn} be the Fibonacci sequence defined by f0 = 0, f1 = 1, fn+2 = fn+1 + fn If F(x) = fnx

Let {fn} be the Fibonacci sequence defined by
f0 = 0, f1 = 1, fn+2 = fn+1 + fn
If F(x) =
fnx

Show that
F(x) - xF(x) - x2F(x) = x
And then use this fact to obtain a simple formula for F(x)?

fnx"

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