Suppose that T(0) = a and T(1) b are 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)...

Extracted text: Suppose that T(0) = a and T(1) b are 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 F(x) = T(n)x" n=0 Use the recurrence relation on T to find an cquation for F.