Prove that a(n) = L(n + 1)t-tJ where t-t = (- 1 + ./5)/2.
Chapter 4, Problem 4.68(choose chapter or problem)
Prove that a(n) = L(n + 1)t-tJ where t-t = (- 1 + ./5)/2. [Hint: First show for all n > 0 that (t-tn - Lt-tnJ) + (t-t2 n - Lt-t2 nJ) = 1. Then show for all real numbers a with 0 :::s a < 1 and a =11 - t-t that L(1 + t-t)(I - a)J + La + t-t J = 1, considering the cases 0 :::s a < 1 - t-t and 1 - t-t < a < 1 separately.]
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