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Determine whether the statement is true or false and why your answer is correct. If lim an L, then lim a2n + 1 = L. n→8 n→∞ False. When a sequence converges, the odd terms can have a different limit than the even ones. True. If lim an = L, then as n→∞, 2n+1→∞ SO lim a2n+1 L. n→∞ n18 True. Even if the limit does not exist, all subsequences must approach the same thing. 2L+1. False. lim a2n+1 n→∞ =

Determine whether the statement is true or false and why your answer is correct. If lim an L, then lim a2n + 1 = L. n→8 n→∞ False. When a sequence converges, the odd terms can have a different limit than the even ones. True. If lim an = L, then as n→∞, 2n+1→∞ SO lim a2n+1 L. n→∞ n18 True. Even if the limit does not exist, all subsequences must approach the same thing. 2L+1. False. lim a2n+1 n→∞ =

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 73E
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Determine whether the statement is true or false and why your answer is correct. L, then lim a2n + 1 = L. n→∞ False. When a sequence converges, the odd terms can have a different limit than the even ones. True. If lim an = L, then as n→∞, 2n+1→∞ SO lim a2n+1 = L. n→∞ n→∞ If lim an n→∞ True. Even if the limit does not exist, all subsequences must approach the same thing. False. lim a2n+1 2L+1 n→∞ =
Transcribed Image Text:Determine whether the statement is true or false and why your answer is correct. L, then lim a2n + 1 = L. n→∞ False. When a sequence converges, the odd terms can have a different limit than the even ones. True. If lim an = L, then as n→∞, 2n+1→∞ SO lim a2n+1 = L. n→∞ n→∞ If lim an n→∞ True. Even if the limit does not exist, all subsequences must approach the same thing. False. lim a2n+1 2L+1 n→∞ =
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