Could you please elaborate the following proof more? I understand the basis step, and I get what we're trying to proof in the induction step, my problem is the highlighted part, things are being added and substituted and I have no idea where they come from, could you please explain in detail what they are doing in these steps, what steps they're taking? I want to understand this exact proof Lemma 14.11 Let Sn =integer n.Proofnk=1= 1+11n+-, where ne N. Then S2 ≥1+ for every positive2nWe proceed by induction. For n = 1, $₂¹ = 1 + and so the result holds for n = 1.12k, where ke N. We show that S₂k+1 ≥ 1+Assume that s₂k ≥ 1+that2$2k+1 = 1+12= $₂k +≥ S₂k += S₂k ++12k + 112k+12k2k+112k+112k +212k+1+++S2k +k 1≥1+=+ =1+2 2+1+2k + 12+12k+11ok+1By the Principle of Mathematical Induction, S2″ ≥1+integer n.nINk+12Now observefor every positive

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Answered: Lemma 14.11 Let Sn = integer n. n k=1 =…

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 you please elaborate the following proof more? I understand the basis step, and I get what we're trying to proof in the induction step, my problem is the highlighted part, things are being added and substituted and I have no idea where they come from, could you please explain in detail what they are doing in these steps, what steps they're taking? I want to understand this exact proof