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Alternating series help

  1. Jan 22, 2008 #1
    1. The problem statement, all variables and given/known data

    Determine wheter the series is convergent or divergent. If it convergent, approximate the sum of the series correct to four decimal places.

    heres the equation: http://img251.imageshack.us/img251/2261/46755781zg9.png

    2. Relevant equations



    3. The attempt at a solution

    This appears to be an alternating geometric series,

    Would it be okay to move the exponent k over everything? in other words: ( (-1)/k) )^k

    So then it looks alot like a geometric series, so then It converges by the rules of an alernating series, it is decreasing and it is approaching zero.

    So then to find its sum, i would do so by geometric series right?

    first term would be starting at k = 2, so: 1/2?

    then use 1/2 divided by 1 -r

    Am i on the right track? what is r??? is it also, 1/2?
     
  2. jcsd
  3. Jan 22, 2008 #2

    Pyrrhus

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    Homework Helper

    Yes you can use k as the exponent of the whole because of the distributive property of exponentiation.
     
  4. Jan 22, 2008 #3
    how about the rest of what i'm doing here, this was my best hypothesis to approach the problem. I need help with the common ratio. i'm not sure what to use if its k^k ?
     
  5. Jan 22, 2008 #4

    dynamicsolo

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    Homework Helper

    It isn't a geometric series because such series has a constant ratio between successive terms. However, that gives you a clue to the proof of its convergence. (Try a comparison test.) As for the estimate of the sum, do they want an analytical proof of some sort or just something carried out on a calculator (how many terms do you need to get to a precision of 10^-4 ?)
     
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