In this problem you will use mathematical induction to prove (for all integers n >= 1): P(n): 1*2*3 + 2*3*4 + ... + n(n+1)(n+2) = n(n+1)(n+2)(n+3)/4 (We will complete the base case for you as follows.) Consider the base case when n = 1. In this case, the summation on the left side of P(n) contains just the first term (1*2*3) and has the value 6. When n has value 1, the right side of P(n) becomes 1(1+1)(1+2)(1+3)/4 and also has the value 6. Thus, the statement is true for the base case. Complete parts a-d below to show that the statement works for the inductive case. a. State the inductive hypothesis. b. State what is to be proven in the inductive step. c. Give the result of using the inductive hypothesis (from part a) to make a substitution into the summation side of part b. d. Use algebra to show that the result for part c is equivalent to the right side of part b.