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Look at the following proposition about a natural number n: 2 + 3 < 4 2, and n=3. (a.) Investigate if this proposition is-true-or-false forn 0, 1, (b.) Prove by simple induction on 72 that the proposition is true for all n ≥ 2.

Look at the following proposition about a natural number n: 2 + 3 < 4 2, and n=3. (a.) Investigate if this proposition is-true-or-false forn 0, 1, (b.) Prove by simple induction on 72 that the proposition is true for all n ≥ 2.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.5: Mathematical Induction
Problem 42E
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I need more explanation to understand "Inductive Step"

Inductive Step: Now, 2k+1 + 3k+12k 2+3.3 =2k (4-2) + 3k (4 – 1) =4.2k +4.3k <4 (2k + 3k) <4.4k =4k+1 (2k+1+3k) ?? Thus, for n = k + 1, the statement P (k+ 1) is true whenever P (k). Also, the basis step confirms that P (2) is true.
Transcribed Image Text:Inductive Step: Now, 2k+1 + 3k+12k 2+3.3 =2k (4-2) + 3k (4 – 1) =4.2k +4.3k <4 (2k + 3k) <4.4k =4k+1 (2k+1+3k) ?? Thus, for n = k + 1, the statement P (k+ 1) is true whenever P (k). Also, the basis step confirms that P (2) is true.
Look at the following proposition about a natural number n: 2n + 3 < 4n 2, and n-3. (a.) Investigate if this proposition is true or false for n=0, n=1, (b.) Prove by simple induction on n that the proposition is true for all n ≥ 2.
Transcribed Image Text:Look at the following proposition about a natural number n: 2n + 3 < 4n 2, and n-3. (a.) Investigate if this proposition is true or false for n=0, n=1, (b.) Prove by simple induction on n that the proposition is true for all n ≥ 2.
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