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Math Help - Another Arithmetic series question.....

  1. #1
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    Another Arithmetic series question.....

    If the limiting sum of the series a +ar + ar^2 +......... is x, then show S_n = [x^n - (x-a)^n]/ x^(n-1)

    Thanks for any help......
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  2. #2
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    Quote Originally Posted by anonymous_maths View Post
    If the limiting sum of the series a +ar + ar^2 +......... is x, then show S_n = [x^n - (x-a)^n]/ x^(n-1)

    Thanks for any help......
    S_{\infty} = \frac{a}{1 - r} \Rightarrow x = \frac{a}{1-r}. Re-arrange to make r the subject.

    Substitute this expression for r into the usual formula for S_n and simplify.
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