Math 3000 Lectures 7 & 8

Mathematical Induction

Recursion

  1. Fibonacci Numbers
  2. Tower of Hanoi
  3. Let x1 = 1, x2 = 1 and for n 2, xn+1 = xn + 2xn-1. Prove that xn is divisible by 3 iff n is divisible by 3.
  4. F1= F2 = 1, Fn+2 = Fn+1 + Fn + Fn+1Fn.
    Prove that Fn = 2f(n) - 1 where f(n) is the nth Fibonacci number.