3. Numeracy: Suppose we define a function on the natural numbers, where f(0) = 1 and f(n) = nf(n 1) for n 1. (a) Compute f(1), f(2), f(3), . . . , f(10) (using a calculator as necessary). (b) Find a closed form expression for f(n); that is, a way of computing f(n) without having to compute f(n 1). Use this to compute f(100). (c) If n and k are natural numbers with k < n, write (n)(n 1)(n 2) (n k + 1) using only f and divison.