Mathematical induction:

If n is an integer greater than or equal to 1, then the function nines(n) returns an integer made up of n 9s. For example:

nines(1)	=	9
nines(2)	=	99
nines(3)	=	999
nines(4)	=	9999

Let P(n) [nines(n) + 1 = 10ⁿ]. Prove that P(n) is true for all n 1, by mathematical induction. Use the induction schema [P(1) k [P(k) P(k + 1)]] n P(n).

1. (5 points.) What is the base case, P(1)?

2. (5 points.) What is the inductive case, k [P(k) P(k + 1)]?

3. (10 points.) Use your answers from questions 1 and 2 to construct the proof.