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Math Help - Prove or disprove sequences

  1. #1
    MHF Contributor harish21's Avatar
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    Prove or disprove sequences

    1. If the sequence {an^2} converges, then the sequence {an} also converges.

    Is this true or false?
    I think it is true because if {an^2} converges to a number a^2, i.e. |an^2-a^2| < e, then {an}will converge to a,which is the square root of a^2?

    Any suggestions or corrections?
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  2. #2
    MHF Contributor chisigma's Avatar
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    The sequence a_{n}= (-1)^{n} doesn't converge... its square a_{n}^{2}=1 ? ...
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  3. #3
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by chisigma View Post
    The sequence a_{n}= (-1)^{n} doesn't converge... its square a_{n}^{2}=1 ? ...
    so an^2 converges and we have a contradiction..
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