Question: The sequence {fn} is defined recursively by f 1 = 1, f 2 = 1, and f n = f n-1 +f n-2 , for

The sequence {fn} is defined recursively by f₁ = 1, f₂ = 1, and f_n = f_n-1+f_n-2, for n 3. Define the sequence {r_n} of ratios by setting r_n = f_n+1/f_n, n 1.

(a)Use the definition of the sequence {f_n} to give a recursive definition of the sequence {r_n}.

(b) It is known that the sequence {r_n} converges. Find its limit R.

1/f_n

n=1

converges conditionally, converges absolutely, or diverges.

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