#6 part c 8:50AaSection 4.1. Convergence 1694.1 EXERCISESExercises marked with * are used in later sections, and exercises marked with *have hints or solutions in the back of the book.1. Mark each statement True or False. Justify cach answer.(a) If (s.) is a sequence and s, S, then /-.(b) Ifs, s, then for every e> 0 there exists Ne N such that n2 N implies(c) If s, k and t, → k, then s, -t, for all n e N.(d) Every convergent sequence is bounded.2. Mark each statement True or False. Justify each answer.(a) Ifs, 0, then for every e> 0 there exists Ne N such that n2 N implies(b) If for every e>0 there exists Ne N such thatn2 N implies s, < 6, thenS.0.(c) Given sequences (s,) and (a.), if for some s e R, k> 0 and m eN wehave s,-sS kla. for all n> m, then lim s, =s.(d) Ifs, →s and s, 1, then s = t.3. Write out the first seven terms of each sequence.(a) a, -n *(-1)"(b) b, =2n+1(c) c,- cosс, соs(d) d,3n-14. Find k>0 and meN so that 6n' + 17n s kn' for all integers n2 m.5. Find k>0 and me N so that n- 7n 2 ku for all integers n2m.6. Using only Definition 4.1.2, prove the following.(a) For any real number k, lim, (k/n) - 0.*(b) For any real number k > 0, lim,(1/n) = 0.() lim An +14n+3(d) lim Sin -0(d) limn+3(e) lim-n-13n+2(f) lim =0n +n-37. Using any of the results in this section, prove the following.Sn -6(a) lim=02+ 3n(b) lim2n - 7n6n +3n= 32n -5(c) lim(d) lim V<>169ReaderContentsNotebookBookmarksFlashcardsIK

Name: #6 part c 8:50AaSection 4.1. Convergence 1694.1 EXERCISESExercises mar
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Description: #6 part c 8:50AaSection 4.1. Convergence 1694.1 EXERCISESExercises marked with * are used in later sections, and exercises marked with *have hints or solutions in the back of the book.1. Mark each statement True or False. Justify cach answer.(a) If (