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  3. let {an} be a bounded sequence. in this question,

Let {an} be a bounded sequence. In this question, you will prove that there exists a...

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Advance Math

  1. Let {an} be a bounded sequence. In this question,you will prove that there exists a convergent subsequence.

Define a crest of the sequence to be aterm am that is greater than all subsequent terms. That is,am > an for all n > m

  1. (a) Suppose {an} has infinitely many crests. Provethat the crests form a convergent subsequence.
  2. (b) Suppose {an} has only finitely many crests. Letan1 be a term with no subsequent crests. Construct aconvergent subsequence with an1 as the first term.

Answer & Explanation Solved by verified expert
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The solution is given below In part a the subsequence    See Answer
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