C Generating Function Show That The Generating Function Of The

(a) The Fibonacci numbers are recursively defined by a0 = a1 = 1, an+1 + an + an-1 if Find the limit of the sequence (an+1/an.)
(b) Fibonacci’s rabbit problem. Compute a list of a1, ··· a12. Show that is the number of pairs of rabbits after 12 months if initially there is 1 pair and each pair generates 1 pair per month, beginning in the second month of existence (no deaths occurring).

(c) Generating function. Show that the generating function of the Fibonacci number is f(z) = 1/(1 – z – z2) ; that is, if a power series (1) represents this f(z), its coefficients must be the Fibonacci number and conversely.

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