37. Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. a. Suppose 0 < a

Algebra: Structure And Method, Book 1
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Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
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Chapter1: Introduction To Algebra
Section1.4: Translating Words Into Symbols
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37. Explain why or why not Determine whether the following statements are true and give an explanation or
counterexample.
a. Suppose 0 < ak <bk. If Σak converges, then Σb converges.
b. Suppose 0 < a <bk. If Σak diverges, then Σb diverges.
c. Suppose 0 <bk <ck <ak. If Σak converges, then bk and Σck converge.
∞
d. When applying the Limit Comparison Test, an appropriate comparison series for
k =
k² + 2k + 1
₁k³ + 5k +7
is Σ 1/1 10
k = 1k
Transcribed Image Text:37. Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. a. Suppose 0 < ak <bk. If Σak converges, then Σb converges. b. Suppose 0 < a <bk. If Σak diverges, then Σb diverges. c. Suppose 0 <bk <ck <ak. If Σak converges, then bk and Σck converge. ∞ d. When applying the Limit Comparison Test, an appropriate comparison series for k = k² + 2k + 1 ₁k³ + 5k +7 is Σ 1/1 10 k = 1k
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