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Problem 4. Let a, = 2, a2= 9, and an= 2an-1+ 3an-2, for n > 3. Use mathematical induction to show that an < 3" for all positive integersn.

Problem 4. Let a, = 2, a2= 9, and an= 2an-1+ 3an-2, for n > 3. Use mathematical induction to show that an < 3" for all positive integersn.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Could solve the problem 4 with the way that I attached photo (with base/inductive steps). please?

 

Problem 4. Let a, = 2, a2= 9, and an= 2an-1+3an-2, for n > 3. Use mathematical induction to show that an< 3" for all positive integersn.
Transcribed Image Text:Problem 4. Let a, = 2, a2= 9, and an= 2an-1+3an-2, for n > 3. Use mathematical induction to show that an< 3" for all positive integersn.
Date. Page. n>/ Prve Hhat § F;' = Fn. Fatt, 2. F,"+ F," +F t + Fa Eo i Enti Basis step: P() 2. 1=1 a True Pci) is trie stot Inductive stes:s Assmne that Assume that plCk) is true forok>/ p'(k) is true hor k>/ 2. 2. F. 2. + Fk PCは+I) + Fk + Fr t plove that 7P(kH): Ę + F t F,'+ F,'+ wi Fkt Fir is frue +FFH Me want to 2. 2. 2. 2. Fkt2 Fr+K(F,+FKti True, therefore, P(K) → p(Kt!) is tree 2. -Feti Fk+2 ニ → P(kt) is A Therelore I F Fn Fati is true for hzl 2. tち t is true 2. where nis positine $ integer and to s the Fibonacci number. a nth 2.
Transcribed Image Text:Date. Page. n>/ Prve Hhat § F;' = Fn. Fatt, 2. F,"+ F," +F t + Fa Eo i Enti Basis step: P() 2. 1=1 a True Pci) is trie stot Inductive stes:s Assmne that Assume that plCk) is true forok>/ p'(k) is true hor k>/ 2. 2. F. 2. + Fk PCは+I) + Fk + Fr t plove that 7P(kH): Ę + F t F,'+ F,'+ wi Fkt Fir is frue +FFH Me want to 2. 2. 2. 2. Fkt2 Fr+K(F,+FKti True, therefore, P(K) → p(Kt!) is tree 2. -Feti Fk+2 ニ → P(kt) is A Therelore I F Fn Fati is true for hzl 2. tち t is true 2. where nis positine $ integer and to s the Fibonacci number. a nth 2.
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