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Math Help - Converging Sequence Theorem

  1. #1
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    Converging Sequence Theorem

    Prove that if the sequence {An} converges to A, then the sequence {|An|} converges to |A|. And is the converse true?

    This is for my calculus class and it needs to be in proof format. Thank you!
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  2. #2
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    Quote Originally Posted by Mush89 View Post
    Prove that if the sequence {An} converges to A, then the sequence {|An|} converges to |A|. And is the converse true?
    This is for my calculus class and it needs to be in proof format.
    Then you need to write out a formal proof for yourself.
    Here is what it will be based upon, \left||x|-|y|\right|\le |x-y|.

    Show us what you come up with.
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  3. #3
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    I was going to plug that inequality into the definition of a limit, but is that going in the wrong direction?
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    Quote Originally Posted by Mush89 View Post
    I was going to plug that inequality into the definition of a limit, but is that going in the wrong direction?
    It absolutely does not.
    The sequence (a_n) converges. That is the one we have control over. We use it the get a handle on the sequence \left|(a_n)\right|
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