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Series 5.

  1. Nov 19, 2007 #1
    1. The problem statement, all variables and given/known data
    Determine whether the series converges absolutely,converges conditionally or diverges.

    where p is a some parameter

    3. The attempt at a solution


    [tex]\sum_{n=1}^{\infty}\frac{1}{n^{2p}}[/tex] converges for p>1/2

    [tex]\sum_{n=1}^{\infty}\frac{(-1)^n}{n^p}[/tex] converges absolutely for p>1

    My answer is the series converges for p>1/2

    for [tex]\frac{1}{2}<p\leq 1[/tex] it converges conditionally

    for [tex]p>1[/tex] it converges absolutely
  2. jcsd
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