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Math Help - Series Problem

  1. #1
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    Series Problem

    Problem:

    Consider the following infinite series.

    3 - 3x + 3x^2 - 3x^3 + 3x^4 - ...


    (a) For what values of x will the sum of the series be a finite value?
    (b) Find the value of the infinite series for x in the interval in part (a).

    Could somebody explain how this is done? I really don't understand where to even start...
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  2. #2
    Super Member 11rdc11's Avatar
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    Quote Originally Posted by lysserloo View Post
    Problem:

    Consider the following infinite series.

    3 - 3x + 3x^2 - 3x^3 + 3x^4 - ...


    (a) For what values of x will the sum of the series be a finite value?
    (b) Find the value of the infinite series for x in the interval in part (a).

    Could somebody explain how this is done? I really don't understand where to even start...
    It is a geometric series.
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  3. #3
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    I understand that, but I don't understand how to find the sum when x has to be in an interval from -1 to 1 (the answer to part a).

    How do I solve when x is an interval and not a set number?
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  4. #4
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    Quote Originally Posted by lysserloo View Post
    I understand that, but I don't understand how to find the sum when x has to be in an interval from -1 to 1 (the answer to part a).

    How do I solve when x is an interval and not a set number?
    You should know then that a = 3 and r = -x. Now, what is the condition on r for an inifinite geometric series to have a finite value ....?
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