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Math Help - Clarification of Alternating Series test

  1. #1
    Super Member angel.white's Avatar
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    Clarification of Alternating Series test

    I need to determine whether \sum_{n=2}^\infty (-1)^n \frac {x^n}{4^n ln(n)} diverges at x= -4, and x=4.

    I want to use the alternating series test, but my book defines it as starting at n=1, not n=2 like in my problem.

    Can I use the test as it is? Do I need to manipulate it? If I need to manipulate it, would this be a valid manipulation?:
    = \sum_{n=1}^\infty (-1)^{n+1} \frac {x^{n+1}}{4^{n+1} ln(n+1)} = \sum_{n=1}^\infty (-1)^{n-1} \frac {x^{n+1}}{4^{n+1} ln(n+1)}

    I'm fairly certian it is, but I'm still a tad bit shaky with these.
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  2. #2
    Moo
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    Hello,

    Adding or removing a finite number of terms is not important when it's about to talk about convergence and divergence... I think... This has to deal with Cauchy's criteria. But it has been months since i have done this.

    Otherwise, yeah, a variable change can fit in
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  3. #3
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    Quote Originally Posted by Moo View Post
    Adding or removing a finite number of terms is not important when it's about to talk about convergence and divergence... I think...
    It is okay
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