Can you help me find the mistake? My teacher said there is an equal sign that should be inequality but I can't find it # 8Suppose that ho ih, ihz.- is a sequencedefined as follows.h, =1 ,h, = 2, h2 = 3, hz =%3Dhx =hk-i t hk -2 the-3 for each integer K3a) Prore that ha E 3" for every integerProof (by strong induction)P(0):" h,= 30" ?Pli): "h,=3'" ?P(2): "h2 =32"Assume PCi) is true for 1E i sk%3D1 3° v2 3' vNTSPCK+1) IS TAssumeNTS: h+1 3hk-143K-hk-2 63K-2kk^2by Subshitution*3K-2-2- (3*-3+1)(3*-2)- (13)(3*-2)(2.7)(3*-2)(3)(3**)by algeb rm. There's one (what I think is obvious) equality thatshould be inequality.

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E 3* + 3K +3K-2 Suppose that ho ih, ihz.. is a sequence # 8 defined as follows. h, =1 ,h, = 2, ha = 3 he =hk-i t hk -2 the-3 for each integer K3 a) Prove that hn E 3^ for every integer %3D Proof (by strong induction) P(O):" h,= 30" ? Pli): "h,=3'"? P(2): "h2 =32" Assume PCi) is true for IE isk 1 3° v 2 3' v %3D NTS PCK+1) IS T Assume hk 3* Let kE Z"ƏkZ2 NTS: hx+l=3k hk-143k- hk-2 63K-2 hKt1 = h +hky the k^2 by Subshitution 3 (3-)+3(3*3)+3*2 : (3*+3+1)(3*-2) - (13)(3*-2) (2.7)(3-3) (3)(3**) by algeb rm.

E 3* + 3K +3K-2 Suppose that ho ih, ihz.. is a sequence # 8 defined as follows. h, =1 ,h, = 2, ha = 3 he =hk-i t hk -2 the-3 for each integer K3 a) Prove that hn E 3^ for every integer %3D Proof (by strong induction) P(O):" h,= 30" ? Pli): "h,=3'"? P(2): "h2 =32" Assume PCi) is true for IE isk 1 3° v 2 3' v %3D NTS PCK+1) IS T Assume hk 3* Let kE Z"ƏkZ2 NTS: hx+l=3k hk-143k- hk-2 63K-2 hKt1 = h +hky the k^2 by Subshitution 3 (3-)+3(33)+32 : (3+3+1)(3-2) - (13)(3*-2) (2.7)(3-3) (3)(3**) by algeb rm.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.2: Mathematical Induction

Problem 52E: Given the recursively defined sequence a1=1,a2=3,a3=9, and an=an13an2+9an3, use complete induction...

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