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Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
- Use 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_forward49. a. The binomial coefficients are defined in Exercise of Section. Use induction on to prove that if is a prime integer, then is a factor of for . (From Exercise of Section, it is known that is an integer.) b. Use induction on to prove that if is a prime integer, then is a factor of .arrow_forwardGiven the recursively defined sequence a1=1,a2=3,a3=9, and an=an13an2+9an3, use complete induction to prove that an=3n1 for all positive integers n.arrow_forward
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