(a) The Fibonacci numbers are recursively defined by a₀ = a₁ = 1, a_n+1 + a_n + a_n-1 if Find the limit of the sequence (a_n+1/a_n.)
(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.