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Some tips or help on this?

  1. Feb 13, 2005 #1
    so I need to show that Z(n) := ((a^n + b^n))^(1/n), show that the limit of Z(n) = b, given 0 < a < b.

    been going back and forth and cant think of anything, but here are some random thoughts.

    -basically, if I look at this in terms of definition, it is saying to show that |Z(n) - b | < episilon
    - a < b means a^n < b^n
    -can I conlcude that b is an upperbound?

    are any of these important to solving this proof?

    any ideas guys? I'm just stumped and dotn know where to start.
     
  2. jcsd
  3. Feb 13, 2005 #2

    dextercioby

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    HINT:Use the fact that the limit and the natural logarithm commute...It should come out pretty easily.

    Daniel.
     
  4. Feb 13, 2005 #3
    Forget the logarithms. You know that
    Z(n) < (b^n + b^n) ^ (1/n) = 2^(1/n) * b
    and
    Z(n) > (b^n ) ^ (1/n) = b

    Just evaluate the limits...
     
    Last edited: Feb 13, 2005
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