Concept explainers
For Exercises 17—24, use mathematical Induction to prove the given statement for all positive integers n. (See Example 3)
19.
Want to see the full answer?
Check out a sample textbook solutionChapter 12 Solutions
College Algebra & Trigonometry - Standalone book
- Prove by induction that 1+2n3n for n1.arrow_forwardUse generalized induction and Exercise 43 to prove that n22n for all integers n5. (In connection with this result, see the discussion of counterexamples in the Appendix.) 1+2n2n for all integers n3arrow_forwardThe first question: Use the principle of mathematical induction to prove the validity of the following report:arrow_forward
- Use mathematical induction to prove the following formulae for every positive integer na) 1 / 1.2.3 + 1 / 2.3.4 + 1 / 3.4.5 + ⋯ + 1 / n(n + 1)(n + 2) = n(n + 3) / 4(n + 1)(n + 2)Ensure that you explain the steps taken. b) 13 + 33 + 53 +⋯ + (2n − 1)3 = n2 (2n2 -1)Ensure that you explain the steps taken.arrow_forwardProve my mathematical induction 1³+2³+3³+... +n³=[n(n+1)/2] ²arrow_forwardProve that n2 > 2n + 1 for n ≥ 3. Show that the formula is true for n = 3 and then use step 2 of mathematical induction.arrow_forward
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningElements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,