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Math Help - geometric series problem

  1. #1
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    geometric series problem

    Given the infinite series \sum_{r=0} ^\infty\left ( \frac{1-x}{x} \right )^r

    a)show that the series is a geometric series

    b)determine the set of value of x(x>0) so that the sum to infinity , S_{\infty} exist

    c)if x = 2, find the sum of the first five terms, S_5 and S_{\infty}.Show that S_5 : S_{\infty} = 33:32
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  2. #2
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    Re: geometric series problem

    This problem is solved in a standard way, so you need to show some effort.

    \sum_{r=0}^\infty a^r converges iff |a|<1. When you are looking for the set of x for which the series converges, remember that an equality changes sign when multiplied by a negative number.
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  3. #3
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    Re: geometric series problem

    what should i do sir?
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  4. #4
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    Re: geometric series problem

    Quote Originally Posted by mastermin346 View Post
    what should i do sir?
    Show some effort.
    What is the formula for S_5  = \sum\limits_{k = 0}^5 {r^k }~?
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  5. #5
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    Re: geometric series problem

    For part (a), study the definition of geometric progression and geometric series.

    For part (b), I gave you a hint. I used the term "converges." By definition, a series converges iff its sum to infinity exists.
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