#15 9, determine whether or nota method of proof for the given statement. Note: You don't have to see ifthe inductive argument actually works, just state whether or not the statementreflects the type of question for which induction would be an option.5. 11 n is any integer, then 8 divides 5" +2.3"-+1.6. If n is a positive integer, then 2" > n.1. For every integer n> 1, 1(1!) + 2(2!) ++ n(n!) (n+1)! - 1.8. If n is an integer, then n2+n+1 is odd.9. If r is a real number, then vr2 r.VNow we ask that you try to construct some induction proofs on your own:10. Prove that for any integer n, n > 1, n3 + 5n +6 is divisible by 3.11. Prove that for any natural number n, 2+5+8+... + (3n- 1) =n(3n+1)12. Prove that for any natural number n, 5"-1 is divisible by 4.13. Prove that for every natural number n, 20 + 2+..+ 2"2n+1 1.%3D14. Prove that for any natural number n, 7|(9"-2").15. Prove that for each natural number n,n(4n-3)(4n-...4n+1'16. Prove that for each natural number n, 21| (4"+1 +52n-1).17. Prove that for each natural number n, + + +... + = 22十218. Let r E R, r 1. Prove that for any natural number n,1+r+x + ... + x" =n+1_r-1

Name: #15 9, determine whether or nota method of proof for the given stateme
Uploaded: 2024-03-05T11:52:21.000Z
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Description: #15 9, determine whether or nota method of proof for the given statement. Note: You don't have to see ifthe inductive argument actually works, just state whether or not the statementreflects the type of question for which induction would be an option