r2 - r - 1 =0. The smaller of those roots is r1 = and the larger is r2 = (You wa

Question

r2 - r - 1 =0. The smaller of those roots is r1 = and the larger is r2 = (You want to use exact expressions for those roots.) Its clear that any sequence of the form where A and B arc arbitrary numbers, also satisfy the difference equation Find the particular values of A and B which make fn satisfy the starting conditions. Thus A = , and the larger is B = Use your values of 4 and B to compute f7 = and f8 = . (Compare these with the values computed directly from the difference equation.) Finally, compute the limit Nothing compares to the power of mathematical thought!

Explanation / Answer

r1 = 1/2(1-sqrt(5))

r2 = 1/2(1+sqrt(5))

A = -1/sqrt(5)

B = 1/sqrt(5)

f7 = 13

f8 = 21

L = 1/2(1+/- sqrt(5))

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