Determine whether each of the following statements is true. If true, prove it. If false, give a counterexample. (a) Let an → o and b, → -0o. Then an – bn → 0. (b) Let a, +∞ and b, + oo. Then a,bn → 00. (c) Let an 0o and b, be unbounded above. Then an + ba + 00. (d) Let a, + 0 for all n, and a, → 0. Then 1/a, → 0.
Determine whether each of the following statements is true. If true, prove it. If false, give a counterexample. (a) Let an → o and b, → -0o. Then an – bn → 0. (b) Let a, +∞ and b, + oo. Then a,bn → 00. (c) Let an 0o and b, be unbounded above. Then an + ba + 00. (d) Let a, + 0 for all n, and a, → 0. Then 1/a, → 0.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 39E
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