Q2. [5 points] Induction. For each integer n 2 1, define the sum S(n) as follows: S(n) = II 2i - 1 1 3 5 2n-1 i=1 2 4 6 2n For example S(1) = II2 - 2 - i. Compared the each of the following values of S(n) with f(n) = 3nti S(3) = f (3) = S ( 4) = f ( 4 ) = ii.Prove that the proposition P(n) is true for all n > 1 using a Proof by induction. The proposition P(n) below. For each integer n > 1, let P(n) be the proposition defined as follows: P(n) : S(n) = II 2i - 1 1 3 5 2n - 1 2i 2 4 6 2n i=1 V3n + 1 You must clearly state your Induction Hypothesis and indicate when it is used during the proof of your Induction Step. As usual you must declare what each variable in your solution represents and make it clear whether each step of your proof is an assumption, something you are about to prove, or something that follows from a previous step or definition, etc. Attach additional paper if necessary