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Homework Help: For the following power series: ∑ (4^n x^n)/([log(n+1)]^(n)

  1. Sep 27, 2010 #1
    For the following power series, find

    ∑ (4^n x^n)/([log(n+1)]^(n)

    (a) the radius of convergence
    (b) the interval of convergence, discussing the endpoint convergence when
    the radius of convergence is finite.

    I wanted to know whether my solution is write, is it possible for somone to check it for me. Thank You

    Due to the n-th powers, we use the root test.

    r = lim(n-->∞) |4^n x^n / [log(n+1)]^n|^(1/n)
    = lim(n-->∞) 4|x| / log(n+1)
    = 0 for all x.

    a) radius of convg= 0
    b) interval of convg=0

    since the series is infinte
  2. jcsd
  3. Sep 27, 2010 #2


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    Gold Member

    Are you sure you have read what the root test tells you correctly?
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