Suppose we define a function on the natural numbers, where f(0) = 1 and f(n) = nf(n 1) for n 1.

Compute f(1),f(2),f(3),...,f(10) (using a calculator as necessary).

Find a closed form expression for f(n); that is, a way of computing f(n) without having to compute f(n1).

Use this to compute f(100).

If n and k are natural numbers with k < n, write