Cauchy and sequences
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I need following question to be answered.
Please mention each and every step. Please explain every thing.
Text Book:- Taylor & Menon.
Page 523 Exercise Problem.
Page 526 Exercise Problem
Thanking you
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Solution Summary
This shows how to prove that Cauchy's condition is fulfilled and complete a proof regarding a set and intervals.
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Please see the attachment.
Page 523
Proof:
Since , and for , then we have
Then we get the absolute value on both sides and get
In general, we have
Now we consider and without generality, we assume , where is a nonnegative integer. Then we have
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