Please answer, thank you!Instruction:INDUCTIVE REASONING. The following use inductive reasoning to arrive at a conclusion. Give a counterexample if the conclusion is not valid. Kyla investigated the difference of squares ofconsecutive counting numbers as follows:22-1² = 332-22 = 542-3²2 = 752-42 = 9She concluded that 5012-5002= 1001. And, forany positive integer n, n²-(n-1)2 = 2n-1.

Answered: Image /qna-images/answer/8a592aa0-2beb-4552-ba5d-85b012360af9.jpg

Kyla investigated the difference of squares of consecutive counting numbers as follows: 22-1² = 3 32-22 = 5 42-32= 7 52-42 = 9 She concluded that 5012-5002= 1001. And, for any positive integer n, n²-(n-1)² = 2n-1._

Kyla investigated the difference of squares of consecutive counting numbers as follows: 22-1² = 3 32-22 = 5 42-32= 7 52-42 = 9 She concluded that 5012-5002= 1001. And, for any positive integer n, n²-(n-1)² = 2n-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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Question

Please answer, thank you! Instruction: INDUCTIVE REASONING. The following use inductive reasoning to arrive at a conclusion. Give a counterexample if the conclusion is not valid.

Kyla investigated the difference of squares of
consecutive counting numbers as follows:
22-1² = 3
32-22 = 5
42-3²2 = 7
52-42 = 9
She concluded that 5012-5002= 1001. And, for
any positive integer n, n²-(n-1)2 = 2n-1.

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