Let (sn) be a sequence such that |Sn+1 Sn| <2" for all ne N. Prove (sn) is a Cauchy sequence and hence a convergent sequence.
Let (sn) be a sequence such that |Sn+1 Sn| <2" for all ne N. Prove (sn) is a Cauchy sequence and hence a convergent sequence.
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:10.6 (a) Let (sn) be a sequence such that
|Sn+1
Prove (sn) is a Cauchy sequence and hence a convergent
sequence.
-n
Sn| < 2¯n for all ne N.
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