Nice exercise. I think one detail is left out. When setting x equal to the limit of F_(n+1)/F_n, one should show that this limit exists and is finite. One way to do this is to show that the sequence F_(n+1)/F_n is monotonically increasing, which ensures that the limit exists, and bounded, which ensures that the limit is finite.
Nice exercise. I think one detail is left out. When setting x equal to the limit of F_(n+1)/F_n, one should show that this limit exists and is finite. One way to do this is to show that the sequence F_(n+1)/F_n is monotonically increasing, which ensures that the limit exists, and bounded, which ensures that the limit is finite.
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