Do a proof by mathematical induction using the four steps below to show that the following statement is true for every positive integer n:
(2+6+18+...+2*3^{n-1}=3^{n}-1\)
Question 1: Show that the base case is true
Question 2: What is the inductive hypothesis P(k)?
Question 3: Show what you have to prove, that is P(k+1)
Question 4: Prove P(k)P(k+1): (Justify each step)
Solve this question and show each and every step in detail.