Math 2602  B1 , B2                                                                         Homework #3
                                        Due Thursday, September 2, 2004


1. Let a_n be the sequence for which  a₀ = a₁ = 1 , and  a_n = 2a_n-1 + a_n-2 ,  for n > 2.

    i)  Prove that  a_n is odd for all  n > 0 .

   ii)  Prove that  a_n < 3ⁿ  for all  n > 0 .

   iii) Decide whether  a_n > 2ⁿ for all sufficiently large n .  How do you know?