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.