(a) Prove that if the sequence {a„} converges to a, then the sequence {|a„]} converges to |aļ. (Hint: use the Comparison Lemma and the fact that ||z| – ly|| < |1 – y|.) (b) sequence {a„} also converges" is FALSE. Give a counterexample to show that the statement "If the sequence {|a„]} converges, then the (c) Prove that if the sequence {|a„]} converges to 0, then the sequence {a„} also converges to 0.
(a) Prove that if the sequence {a„} converges to a, then the sequence {|a„]} converges to |aļ. (Hint: use the Comparison Lemma and the fact that ||z| – ly|| < |1 – y|.) (b) sequence {a„} also converges" is FALSE. Give a counterexample to show that the statement "If the sequence {|a„]} converges, then the (c) Prove that if the sequence {|a„]} converges to 0, then the sequence {a„} also converges to 0.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
All please
![Do the following.
(a)
use the Comparison Lemma and the fact that ||r| – lyl| < |æ – y|.)
Prove that if the sequence {an} converges to a, then the sequence {la,|} converges to |al. (Hint:
(b)
sequence {a,} also converges" is FALSE.
Give a counterexample to show that the statement "If the sequence {la,|} converges, then the
(c)
Prove that if the sequence {|a,]} converges to 0, then the sequence {a,} also converges to 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F072e444d-1bde-4899-b3c3-9f07885f3d58%2F2c148b8b-cbc7-4d53-9d56-814ce7f48b08%2F81u2ieu_processed.png&w=3840&q=75)
Transcribed Image Text:Do the following.
(a)
use the Comparison Lemma and the fact that ||r| – lyl| < |æ – y|.)
Prove that if the sequence {an} converges to a, then the sequence {la,|} converges to |al. (Hint:
(b)
sequence {a,} also converges" is FALSE.
Give a counterexample to show that the statement "If the sequence {la,|} converges, then the
(c)
Prove that if the sequence {|a,]} converges to 0, then the sequence {a,} also converges to 0.
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