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Math Help - Find the value for x in geometric series

  1. #1
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    Find the value for x in geometric series

    find the range of values for x which the geometric series has a sum to infinity.

    Find the value for x in geometric series-equa.jpg

    sorry i didnt know how to type the problem in here so i screen grab it from word
    but incase you cant see the pic ill type the best i can

    1- [(x-1)/3] + [(x-1)/3]^2 - [(x-1)/3]^3 + ..... if that makes sense

    sorry my typing skills are not so great only just getting used to using word.

    I some how calculated from many hrs that the range of x was between -1.7 to 0.7 but the lecturer told me that the numbers should be whole numbers and maybe with expressions he is quite vague on what im to do sorry if all this babble is of no help.
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    q=-[(x-1)/3] (why?)

    -1<q<1

    solve for x.
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    sorry, not sure what mean.
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    Quote Originally Posted by Darren78 View Post
    sorry, not sure what mean.
    ASZ gave you the required conditions for convergence of the given geometric series ...

    the common ratio of the series, \displaystyle q = -\frac{x-1}{3}, has to satisfy the inequality |q| < 1 in order to be convergent.
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