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Math Help - Alternating Estimation Series Theorem

  1. #1
    Newbie
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    Oct 2009
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    Alternating Estimation Series Theorem

    Hello,

    I am having problems understanding Alternating Series Estimation Theorem...

    http://i39.tinypic.com/k9uwc9.png


    For the 2nd half of the question (finding the natural number of n)... (ignore the equal signs, I was getting desperate), I thought that like the other tests like convergence, limit comparison, etc that
    b_{n+1} < error
    with the error being the 0.004?
    But that is apparently wrong. I double checked my algebra and it is correct... so it is just a signage error.

    If anybody could even give a hint, that would be greatly appreciated... this whole chapter on series and sequences is confusing.

    Thanks a bunch?
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  2. #2
    MHF Contributor

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    Everything is correct but for the last step.

    You want b_n= \frac{1}{3(3^n)+ 7}\le .004 (not "=") and that gives, just as you say, 3^n\ge \frac{1- .004(7)}{3(.004)}= 81.

    Then n= 4, not 3.
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