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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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Question

please do the following.

1. Prove the base case

2. Prove the inductions step, ( Start with the LHS of Sk+1 and prove that it is equal to to RHS of Sk+1)

3.Write a short sentance to justify the reason of the use of the principle of the mathematical induction.

Prove that Sn is true for all natural number n.
n²(n+1)²
13 + 2 + 3 +
+ n'
4.

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I'm habing trouble understanding your reasoning. Specifically, the way you use ei in the induction cases. You are using ei = x or q, which are not necesirally -1, 0 , or 1 as estipulated in the premise.
Please explain every step
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Please read the question and leave notes on the answer where appropriate. Please DO NOT skip any steps. Please double check your answer. DO NOT SUBMIT A TYPED RESPONSE. Please use a hand written response that is LEGABLE. Please review your answer to make sure all steps are clearly visable. Please double check your work. Thank you. PLEASE PROVE THROUGH INDUCTION. Show all your work and please make sure to Justify your answers.