(a) Show that for any integer n 21, 0 ≤ 22n² + 9n²+ 6n ≤ 37nª. Proof: Suppose n is any integer such that n 2 1 We must show that 0 Now, since n is positive Os 22n +9n²+ 6n (Inequality 1) because every term in 22n + 9n² + 6n is positive In addition, 22n4 +9n²+ 6n s 22n² +9n² +6n4 (Inequality 2) because when n 2 1, 9n² s 154-6n 22n +9² +6n 22n +9n²+ 6n X Add like terms on the right-hand side of Inequality 2 to obtain (Inequality 3). s and on s 37 s37² Then use the transitive property of inequality to combine inequalities 1 and 3, and conclude that

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