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How to prove the following:

  1. Apr 19, 2009 #1
    how do i prove that the following series diverges?

    [tex]\sum[/tex](-1)n-1*[tex]\frac{n-1}{n+1}[/tex]*(1/[tex]\sqrt[n]{n}[/tex])

    is it enough to say that

    lim {n->inf} [tex]\frac{n-1}{n+1}[/tex]*(1/[tex]\sqrt[n]{n}[/tex]) is not 0 ???


    i know for regular series this would be okay but what about series with alternating signs??

    how else can i tbe proven??
     
  2. jcsd
  3. Apr 19, 2009 #2
    Yes, an alternating series converges if and only if the limit of the terms go to zero.
     
  4. Apr 19, 2009 #3
    thanks, youve really helped me with this work,
     
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