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Converging series

  1. Jan 21, 2009 #1
    1. The problem statement, all variables and given/known data

    Show that the following series converges:

    2. Relevant equations

    Sum of (from n=1 to infinity) of [3^n + 4^n] / [3^n + 5^n]

    3. The attempt at a solution

    Some help on this question would be much appreciated as i really don't know how to start it. Thanks
  2. jcsd
  3. Jan 21, 2009 #2
    What i would do is break the series into two. then by observing that:



    [tex]3^n+5^n>5^n=>... \frac{4^n}{3^n+5^n}<\left(\frac{4}{5}\right)^n[/tex]
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