ide which of the following statements are true and which are false. Prove the e ones and provide a counterexample for the false ones. an If an converges, then also converges. n an - If an does not converge, then does not converge. n . If an converges and bn is bounded, then anbn converges. . If an converges to zero and bn > 0 for all n E N, then anbn converges.
ide which of the following statements are true and which are false. Prove the e ones and provide a counterexample for the false ones. an If an converges, then also converges. n an - If an does not converge, then does not converge. n . If an converges and bn is bounded, then anbn converges. . If an converges to zero and bn > 0 for all n E N, then anbn converges.
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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Transcribed Image Text:1. Decide which of the following statements are true and which are false. Prove the
true ones and provide a counterexample for the false ones.
an
a. If an converges, then also converges.
n
an
b. If an does not converge, then does not converge.
n
c. If an converges and bn is bounded, then anbn converges.
d. If an converges to zero and bn > 0 for all n E N, then anbn converges.
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Step 1: Definition of bounded and convergent sequence and write some theorem of sequence
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VIEWStep 3: Analysis of statement (b)
VIEWStep 4: Analysis of the statement (c)
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VIEWStep 6: Analysis of the statement (d)
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