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Math Help - what values of p make this serries convergent

  1. #1
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    what values of p make this serries convergent

    Question:what does p need to be for this to be convergent
    sum from 1 to infinity of \frac{(-1)^{n-1}}{n^{p}}
    Answer: p>0
    Confusion: I thought it would have to be p>1 like the "p-series" ( \frac{1}{n^{p}} is convergent for p>1)
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  2. #2
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    Quote Originally Posted by superdude View Post
    Question:what does p need to be for this to be convergent
    sum from 1 to infinity of \frac{(-1)^{n-1}}{n^{p}}
    Answer: p>0
    Confusion: I thought it would have to be p>1 like the "p-series" ( \frac{1}{n^{p}} is convergent for p>1)
    p > 0 forms an alternating series whose nth term approaches 0 ... convergent.

    http://www.mathwords.com/a/alternating_series_test.htm
    Last edited by skeeter; July 31st 2009 at 11:45 AM. Reason: added link
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