Let f₀, f₁, f₂, . . . be the Fibonacci sequence defined as: f₀ = 0, f₁ = 1, and for every k > 1, f_k = f_k-1 + f_{k-2 .}

Use induction to prove that for every n ? 2, f_n ? (1.5)^n-2. Note: youll have two base cases, f₂ and f₃. For the inductive case of f_k+1, youll need to use the inductive hypothesis for both k and k ? 1.