Corrections and Changes to the Third through the Seventh Printings

p. 55, line 7: read: if 0 < |en| < .9, p. 57, display (17): read: if 0 < |en| ≤ .2 • p. 58, Ex. 4.3/2: Omit. (too hard) p. 60, Ans. 4.3/2: read: 1024 p. 63, display (9): delete: > 0 p. 63, line 11 from bottom: read: 5.1/4 p. 68, line 10: replace: hypotheses by: symbols; replace or by and • p. 69, line 9: read: strictly increasing, clearly n1 ≥ 1, n2 ≥ 2, and so on, so eventually lines 11, 13: replace: i 1 by i > N p. 73, line 2: read: an − L p. 73, line 6-: read: and estimate it: use 2.4(4), and (16a), suitably applied to {bn}. •• p. 74, Ex. 5.4/1 Add two preliminary warm-up exercises: a) Prove the theorem if k = 2, and the two subsequences are the sequence of odd terms a2i+1, and the sequence of even terms a2i. b) Prove it in general if k = 2. c) Prove it for any k ≥ 2. • p. 75, Prob. 5-1(a): replace the first line of the “proof” by: Let √ an → M. Then by the Product Theorem for limits, an → M, so that p. 82, Proof (line 2): change: an to xn p. 89, Ex. 6.1/1a: change cn to an p. 89, Ex. 6.1/1b add: to the limit L given in the Nested Intervals Theorem.