#7 c Section 4.1 • Convergenc=1 EXERCISESExercises marked with * are used in later sections, and exercises markehave hints or solutions in the back of the book.1. Mark each statement Trục or False. Justify each answer.(a) If (s,) is a sequence and s; =S, then i =j.(b) If s, → s, then for every e> 0 there exists Ne N such that n2|s, - s|< E.(c) If s, → k and 1, → k, then s, = t, for allne N.(d) Every convergent sequence is bounded.2. Mark each statement True or False. Justify each answer.(a) If s, → 0, then for every ɛ > 0 there exists Ne N such that n2.Sn < E.(b) If for every ɛ > 0 there exists Ne N such that n>N implies smS→ 0.(c) Given sequences (s,) and (a,), if for some s e R, k> 0 and -have |s, - s| < kla, for all n> m, then lim s, = s.(d) If s, → s and s, →1, then s = t.3. Write out the first seven terms of each sequence.(-1)"(b) b, =(а) а, — п? *(c) C, = coS32n +1(d) d, =3n -14. Find k> () and m eN so that 6n' + 17n s kn' for all integers n2 m.5. Find k> 0 and m e N so that n - 7n 2 kn' for all integers n2 m.6. Using only Definition 4.1.2, prove the following.(a) For any real number k, lim, z (k/n) = 0.*(b) For any real number k > 0, lim,, →» (1/n) = 0.(d) lim sin n= 04n+1(c) lim= 4n+3(e) limn+3= 0(f) lim-= 0n +n-3n+2-137. Using any of the results in this section, prove the following.5n - 61(а) lim-(b) lim03-2n - 7n2+3n0 =6n +3n= 3=0 *n+1(с) lim(d) lim2n -5

Name: #7 c Section 4.1 • Convergenc=1 EXERCISESExercises marked with * are u
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Description: #7 c Section 4.1 • Convergenc=1 EXERCISESExercises marked with * are used in later sections, and exercises markehave hints or solutions in the back of the book.1. Mark each statement Trục or False. Justify each answer.(a) If (s,) is a sequence and s;