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Series question

  1. Nov 18, 2007 #1
    1. The problem statement, all variables and given/known data
    Determine whether the series converges or diverges.

    where a,b>0 some parameters.

    3. The attempt at a solution

    [tex]\sum_{n=1}^{\infty}\frac{\ln \left(1+\frac{\sqrt[n]{a}}{n}\right)}{\ln b^n }=\sum_{n=1}^{\infty}\frac{\left(\frac{\sqrt[n]{a}}{n}-O\left(\frac{a^{\frac{2}{n}}}{n^2}\right)\right)}{n\ln b}}[/tex]

    [tex]=\sum_{n=1}^{\infty}\frac{\sqrt[n]{a}}{n^2\ln b}-\sum_{n=1}^{\infty}O\left(\frac{a^{\frac{2}{n}}}{n^3\ln b}\right)[/tex]

    So my solution is series converges.
  2. jcsd
  3. Nov 18, 2007 #2

    Gib Z

    User Avatar
    Homework Helper

    Thats how I would do it as well =]
  4. Nov 18, 2007 #3
    Thank you!!!
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