The Fibonacci sequence is a recursive sequence defined as follows: a_1 = 1 a_2 =

Question

The Fibonacci sequence is a recursive sequence defined as follows: a_1 = 1 a_2 = 1 a_n = a_n-1 + a_n-2 (for n > 3) The sequence starts as 1, 1, 2, 3, 5, 8, 13, 21, ... where each term is the sum of the previous two. Clearly this sequence does not converge, but there is one aspect about it that does. We will construct ratios of successive terms and investigate the limit behavior of those. If a sequence {a_n - 1/a_n-2} converges to some finite limit L, it is reasonable to assume that the sequence { a_n - 2/a_n-1}converges to what value?

Explanation / Answer

Fibonacci sequence is the sequence of choice to study the recurrence a(n) = a(n-1) + a(n-2).

here in this case when we need to find L , it must be less than 1 to get converges

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