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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

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.2: Mathematical Induction
Problem 50E: Show that if the statement 1+2+3+...+n=n(n+1)2+2 is assumed to be true for n=k, the same equation...
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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

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