The sequence {Fn } described by F0 = 1, F1 = 1, and Fn+2 = Fn + Fn+1, if n 0, is called
Chapter 1, Problem 1.3.16(choose chapter or problem)
The sequence {Fn } described by F0 = 1, F1 = 1, and Fn+2 = Fn + Fn+1, if n 0, is called the Fibonacci sequence. Its terms occur naturally in many botanical species, particularly those with petals or scales arranged in the form of a logarithmic spiral. Consider the sequence {xn }, where xn = Fn+1/Fn . Assuming that limn xn = x exists, show that x = (1 + 5)/2. This number is called the golden ratio.
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