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Math Help - Absolute value of a sequence converges then . . .

  1. #1
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    Absolute value of a sequence converges then . . .

    Question:
    Prove or give a counterexample:
    If the absolute value of a sequence is convergent then the sequence is convergent.

    I think this is false, because it should be if the sequence is convergent, then the absolute value is convergent. I think a counterexample is (-1)^n as a counterexample. Does this sound right?

    Thanks.
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  2. #2
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    Re: Absolute value of a sequence converges then . . .

    Quote Originally Posted by CountingPenguins View Post
    Prove or give a counterexample:
    If the absolute value of a sequence is convergent then the sequence is convergent. a counterexample is (-1)^n as a counterexample.
    That is correct.
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