choose all correct answers:1)proof is wrong2) proof is correct.3) the base case is incorrect4)The proof is incorrect because the Inductive Hypothesis was not stated.5) there is a problem with inductive step. Consider the following:Claim:1+n 1+(n+ 1),/1+(n+2),/1+(n+3),/.=n+1.Base case: When n = 0, we have /1+0...=0+ 1, and this is true.||Inductive step: Assume that the identity holds for some n and let us prove it holds for n + 1. Bysquaring both sides we get1+n/1+(n+1),/1+ (n+ 2),/1+ (n+3),/-.=n² + 2n + 1.Subtracting 1 and dividing by n, we get|1+ (n+1),/1+ (n +2),/1+(n+ 3)/..=n+2,which is what we wanted to show. I

Answered: choose all correct answers: 1)proof is…

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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Related questions

Question

choose all correct answers:

1)proof is wrong

2) proof is correct.

3) the base case is incorrect

4)The proof is incorrect because the Inductive Hypothesis was not stated.

5) there is a problem with inductive step.

Consider the following:
Claim:
1+n 1+(n+ 1),/1+(n+2),/1+(n+3),/.=n+1.
Base case: When n = 0, we have /1+0...=0+ 1, and this is true.
||
Inductive step: Assume that the identity holds for some n and let us prove it holds for n + 1. By
squaring both sides we get
1+n/1+(n+1),/1+ (n+ 2),/1+ (n+3),/-.=n² + 2n + 1.
Subtracting 1 and dividing by n, we get
|1+ (n+1),/1+ (n +2),/1+(n+ 3)/..=n+2,
which is what we wanted to show. I

Expert Solution

Step 1

Mathematical induction:

Mathematical induction could be a methodology of proving that a press release, a formula, or a theorem is true for all natural numbers.
The approach entails 2 phases to prove some extent.
It shows that a press release is true for the beginning worth in step one (base step).
It shows that if a press release is true for the ordinal iteration (or variety n), it is likewise true for the (n+1)^th iteration (or variety n+1).