The question is in the image. Please explain and provide an answer to the whole question as well as provide the answers for the blanks in the question. Thank you. Prove the following statement by mathematical induction.For every integer n 2 0, 2" < (n + 2)!.Proof (by mathematical induction): Let P(n) be the inequality 2" < (n + 2)!. We will show that P(n) is true for every integer n 2 0.Show that P(0) is true: Before simplifying, the left-hand side of P(0) isand the right-hand side isThe fact that the statement is true canbe deduced from that fact that 2° = 1.Show that for each integer k 2 0, if P(k) is true, then P(k + 1) is true: Let k be any integer with k 2 0, and suppose that P(k) is true. In other words, suppose that[This is P(k), the inductive hypothesis.]We must show that P(k + 1) is true. P(k + 1) is the inequality. Information about P(k + 1) can be deduced from the following steps. Identify the reason foreach step.2k < (k + 2)!2k. 2 < (k + 2)! · 22k + 1 < (k + 2)! · 22k + 1 < (k + 2)! · (k + 3)2k + 1by the induction hypothesis vby basic algebra---Select------Select---< (k + 3)!---Select---Since 2k + 1< (k + 3)! the inequality for P(k + 1) is --Select--- vwhich completes the inductive step.[Thus both the basis and the inductive steps have been proved, and so the proof by mathematical induction is complete.]

Name: The question is in the image. Please explain and provide an answer to
Uploaded: 2024-03-20T07:07:37.000Z
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Description: The question is in the image. Please explain and provide an answer to the whole question as well as provide the answers for the blanks in the question. Thank you. Prove the following statement by mathematical induction.For every integer n 2 0, 2" < (