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Give an example of such a convergent series

  1. Sep 17, 2008 #1
    1. The problem statement, all variables and given/known data

    Give an example of a convergent series [tex]\Sigma[/tex] z[tex]_{n}[/tex]

    So that for each n in N we have:

    limsup [tex]abs{\frac{z_{n+1}}{z_{n}}}[/tex] is greater than 1
     
  2. jcsd
  3. Sep 17, 2008 #2

    Dick

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    Re: Series

    How about combining the convergent series 2^(-n) and 3^(-n) in a clever way? Hint: alternate terms from each.
     
  4. Sep 18, 2008 #3
    Re: Series

    yeah thx, I used 2^(-n) when n is even and 2^-(n+1 ) when n is odd
     
  5. Sep 18, 2008 #4

    Dick

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    Re: Series

    Something like that will work, but doesn't that just give you limsup=1?
     
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