Please solve this problem in easy way that i can understand. please dont explain to much for this problem Q: What is wrong with the following “proof” of the “fact” that n+3 n+7 for all values of n (besides of course that the thing it is claiming to prove is false)? Proof. Let P(n) be the statement that n + 3 n + 7. We will prove that P(n) is true for all n ∈ N. Assume, for induction that P(k) is true. That is, k + 3 k + 7. We must show that P(k + 1) is true. Now since k + 3 k + 7, add 1 to both sides. This gives k + 3 + 1 k + 7 + 1. Regrouping (k +1)+3 (k +1)+7. But this is simply P(k +1). Thus by the principle of mathematical induction P(n) is true for all n ∈ N. qed
Please solve this problem in easy way that i can understand. please dont explain to much for this problem Q: What is wrong with the following “proof” of the “fact” that n+3 n+7 for all values of n (besides of course that the thing it is claiming to prove is false)? Proof. Let P(n) be the statement that n + 3 n + 7. We will prove that P(n) is true for all n ∈ N. Assume, for induction that P(k) is true. That is, k + 3 k + 7. We must show that P(k + 1) is true. Now since k + 3 k + 7, add 1 to both sides. This gives k + 3 + 1 k + 7 + 1. Regrouping (k +1)+3 (k +1)+7. But this is simply P(k +1). Thus by the principle of mathematical induction P(n) is true for all n ∈ N. qed
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please solve this problem in easy way that i can understand. please dont explain to much for this problem
Q: What is wrong with the following “proof” of the “fact” that n+3 n+7 for all values of n (besides of course that the thing it is claiming to prove is false)? Proof. Let P(n) be the statement that n + 3 n + 7. We will prove that P(n) is true for all n ∈ N. Assume, for induction that P(k) is true. That is, k + 3 k + 7. We must show that P(k + 1) is true. Now since k + 3 k + 7, add 1 to both sides. This gives k + 3 + 1 k + 7 + 1. Regrouping (k +1)+3 (k +1)+7. But this is simply P(k +1). Thus by the principle of mathematical induction P(n) is true for all n ∈ N. qed
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
