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Math Help - Series

  1. #1
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    Series

    Can any one please help me to prove this :

    If the series an is divergent then the series ran is also divergent for any given non-zero real number r.

    I know that the result is true by intuition yet I have a difficulty in giving a rigorous proof.

    Any help would be great!
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  2. #2
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    Re: Series

    Quote Originally Posted by Kristen111111111111111111 View Post
    Can any one please help me to prove this :

    If the series an is divergent then the series ran is also divergent for any given non-zero real number r.

    I know that the result is true by intuition yet I have a difficulty in giving a rigorous proof.

    Any help would be great!
    Series-untitled2.gif
    Last edited by votan; September 29th 2013 at 02:11 PM.
    Thanks from topsquark
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  3. #3
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    Re: Series

    Quote Originally Posted by Kristen111111111111111111 View Post
    Can any one please help me to prove this :

    If the series an is divergent then the series ran is also divergent for any given non-zero real number r.

    I know that the result is true by intuition yet I have a difficulty in giving a rigorous proof.

    Any help would be great!
    For any finite "partial sum" a_1+ a_2+ \cdot\cdot\cdot+ a_n, the corresponding sum for \sum ar_n is ra_1+ ra_2+ \cdot\cdot\cdot+ ra_n= r(a_1+ a_2+ \cdot\cdot\cdot+ r_n).
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