Suppose that T(0) = a and T(1) = b arc some constants. Define the running pairwise average as, for n > 0, T(n + 2) [T(n +1) + T(n) - We are interested in the long term behavior, i.c., what does T(n) look like as n → o? 1) Define the generating function of T as 8. F(s)ΣΤ(n) σ" n=0 Use the recurrence relation on T to find an cquation for F.

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