For my discrete mathematical structures for computer science class. Please answer all the parts. I'll be sure to rate.

4. For each integer n 2 3, let P(n) be the equation (n-2)(n2+2n+3).| ? P(n) 2.3+3.4+ +(n-1),n= 3 (Recall that by definition 2.3+3.4+ (n-1)-n-Xi-1).i.) a. (6 pts) Is P(3) true? Justify your answer. b. (4 pts) In the inductive step of a proof that P(n) is true for all n 2 3, we suppose P(k) is true (that is the inductive hypothesis), and then we show that P(k +1) is true. Fill in the blanks below to write what we suppose and what we must show for this particular equation. Proof that for all integers k 23, if P(k) is true then P(k +1) is true: Let k be any integer that is greater than or equal to 3, and suppose that We must show that c. (5 pts) Finish the proof started in (b) above