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a (a) For all ne N and a # 0, show that an k=1 (b) For a sequence (xn) in R, suppose that there exists an b € (0, 1) such that Xn+1-Xn ≤b" for all n € N. Use part (a) to prove that xnx for some x € R. Note: If 0 < b < 1 then b = for some a > 1. Then use part (a), since a > 10. 1-

a (a) For all ne N and a # 0, show that an k=1 (b) For a sequence (xn) in R, suppose that there exists an b € (0, 1) such that Xn+1-Xn ≤b" for all n € N. Use part (a) to prove that xnx for some x € R. Note: If 0 < b < 1 then b = for some a > 1. Then use part (a), since a > 10. 1-

Advanced Engineering Mathematics
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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a-1 ak 1 an = 1 (a) For all ne N and a # 0, show that k=1 (b) For a sequence (xn) in R, suppose that there exists an b € (0, 1) such that |xn+1-Xn ≤ b for all n € N. Use part (a) to prove that xnx for some x € R. Note: If 0 < b < 1 then b = for some a > 1. Then use part (a), since a > 1 + 0.
Transcribed Image Text:a-1 ak 1 an = 1 (a) For all ne N and a # 0, show that k=1 (b) For a sequence (xn) in R, suppose that there exists an b € (0, 1) such that |xn+1-Xn ≤ b for all n € N. Use part (a) to prove that xnx for some x € R. Note: If 0 < b < 1 then b = for some a > 1. Then use part (a), since a > 1 + 0.
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