Please help me with this two questions. I am having trouble understanding why the answers are incorrect and what the correct answer is. Please provide the correct answer to the following 2 questions belowThank you Arrange the given steps in the correct order to prove that 3" 6, 3k E Click and drag the steps in the correct order to show that 3 divides n³ + 2n whenever n is a positive integer using mathematicalinduction.BASIS STEP:31 (13+2 1), i.e., 3 | 3, so the basis step is true.INDUCTIVE STEP:Suppose that 3 | (k³ + 2k).By the inductive hypothesis, 3 | (k³ + 2k), andcertainly 3 | 3(k² + 1).As the sum of two multiples of 3 is again divisibleby 3, 3 | ((k+1)3 + 2(k + 1)).31 (03+2 0), i.e., 3 | 0, so the basis step is true.(k+1)3 + 2(k + 1) = (k³ + 3k² + 1) + (2k + 2) = (k³ +2k) + 3(k² + 1)(k+1)3 + 2(k+1) = (k³ + 3k² + 1) + (2k + 2) = (k³ +2k) + 3(k² + 1)Suppose that 3 | (k³ + 2k).By the inductive hypothesis, 3 | (k³ + 2k), andcertainly 3 | 3(k² + k + 1).As the sum of two multiples of 3 is again divisibleby 3, 3 | ((k+1)3 + 2(k + 1)).(k+1)3 + 2(k+1) = (k³ + 3k² + 3k+ 1) + (2k + 2) =(k3 + 2k)+3(k² + k + 1)By the inductive hypothesis, 3 | (k³ + 2k), andcertainly 3 | 3(k² + k + 1).31 (13+2 1), i.e., 3 | 3, so the basis step is true.

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Answered: Arrange the given steps in the correct…

Math

Advanced Math

Arrange the given steps in the correct order to prove that 3" 6, 3k E search e

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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