Let p1, p2, p3 … be a sequence defined recursively as follows.pk = pk − 1 + 2 · 3k for each integer k ≥ 2p1 = 2 Use mathematical induction to show that such a sequence satisfies the equation pn = 3n + 1 − 7 for every integer n ≥ 1.Need help with proofing. The selected statement is true because the two sides of the equation equal each other.Show that for every integer k ≥ 1, if P(k) is true then P(k + 1) is true:Let k be any integer with k ≥ 1, and suppose that P(k) is true, where P(k) is the equationPk= 3+1XThis is the inductive hypothesis=We must show that P(k+ 1) is true, where P(k+ 1) is the equation Pk +1The left-hand side of P(k+ 1) is? VPk + 1==P₁3= 3??= 3.3?= 3V?V+2.3- 7.V(1+2) - 7+2.3- 77?by the laws of algebra,which is the right-hand side of P(k+ 1) [as was to be shown].by definition of P₁ P₂ P3¹ ---by inductive hypothesis- 7.

Let p1 , p2 , p3 ... be a sequence defined recursively as fallows pk=pk-1+2.3k for each integer…

Let p1, p2, p3 … be a sequence defined recursively as follows. pk = pk − 1 + 2 · 3k for each integer k ≥ 2 p1 = 2 Use mathematical induction to show that such a sequence satisfies the equation pn = 3n + 1 − 7 for every integer n ≥ 1. Need help with proofing.

Let p1, p2, p3 … be a sequence defined recursively as follows. pk = pk − 1 + 2 · 3k for each integer k ≥ 2 p1 = 2 Use mathematical induction to show that such a sequence satisfies the equation pn = 3n + 1 − 7 for every integer n ≥ 1. Need help with proofing.

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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