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Math Help - Small doubt

  1. #1
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    Small doubt

    Hi

    Does the sequence defined by (-1)^n diverge or oscillate? I know technically it oscillates but in my MCQ options there are 4 options in which oscillation is not given.

    the options are:
    1. diverges
    2. converges
    3. absolutely converges
    4. none of these

    therefore, would the answer be none of these or "Diverges" ?

    P.S: is oscilllation a sub-set of diverging ? (something like if oscillation is happening then it must diverge? )
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  2. #2
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    Quote Originally Posted by champrock View Post
    Hi

    Does the sequence defined by (-1)^n diverge or oscillate? I know technically it oscillates but in my MCQ options there are 4 options in which oscillation is not given.

    the options are:
    1. diverges
    2. converges
    3. absolutely converges
    4. none of these

    therefore, would the answer be none of these or "Diverges" ?

    P.S: is oscilllation a sub-set of diverging ? (something like if oscillation is happening then it must diverge? )
    I would say "diverge" ... a sequence that does not converge to a fixed limit diverges.
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