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Mathematics, 15.02.2020 03:25 fdryktysysmzet3640

The sequence {Fn} described by F0 = 1, F1 = 1, and Fn+2 = Fn+Fn+1, if n ≥ 0, is called a 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 lim --> infinity, xn=x exists, show that x=(1+underrot5)/2.

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The sequence {Fn} described by F0 = 1, F1 = 1, and Fn+2 = Fn+Fn+1, if n ≥ 0, is called a Fibonacci s...

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