Consider the functions fa : N N and fb : N N defined recursively by fa(0) = 0 and for each n N, fa(n + 1) = fa(n) + 2n + 1 fb(0) = 0 and for each n N, fb(n + 1) = 2fb(n) 6 Which of these two functions (if any) equals 2n and which of these functions (if any) equals n2? Use induction to prove the equality or use counterexamples to disprove it