2. Recall that the Fibonacci sequence F(n) is definedby the recurrence relation F(0) = 0, F(1) = 1, and F(n) = F(n − 1)+ F(n − 2) for n > 1.
a. Show that if a = (1+√ 5)/2 and b = (1− √ 5)/2 thena 2−a−1 = b 2−b−1 = 0. Conclude that a 2 = a + 1 and that b 2 = b +1.
b. Prove via induction that F(n) = a n − b n a −b
please neat and show work.
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