Question: (a) For a = (1 + 5)/2 and = (1 - 5)/2, verify that a2 - a-2 = a - = -2 -2.

(a) For a = (1 + √5)/2 and β = (1 - √5)/2, verify that a2 - a-2 = a - β = β-2 -β2.
(b) Prove that F2n = F2n+l - F2n-1, n ≥ 1.
(c) For n ≥ 1, let T be an isosceles trapezoid with bases of length Fn-1 and Fn+1, and sides of length Fn. Prove that the area of T is (√3/4)F2n.

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a b Using the Binet form we have a 2n 2n a from the results in part a F 2n ... View full answer

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