prove by induction Fibonacci sequence: $\forall n \geq 1, F_n \varphi+F_{n-1}=\varphi^n: \varphi \equiv \frac{1+\sqrt{5}}{2}$ ,conclude $\varphi^{10}$

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prove by induction Fibonacci sequence: $\forall n \geq 1, F_n \varphi+F_{n-1}=\varphi^n: \varphi \equiv \frac{1+\sqrt{5}}{2}$ ,conclude $\varphi^{10}$

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