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Math Help - Applications of infinite geometric series

  1. #1
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    Applications of infinite geometric series

    Hi all,

    Just a quick question which I'm stuck on, having never done one before....

    Express in the form a/b: 0.45 (so that both the 4 and 5 are recurring)--0.4444444.......55555555..........

    Thanks in advance!
    Steven
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  2. #2
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    Quote Originally Posted by Stevo_Evo_22 View Post
    Express 0.454545454545 \cdots as a fraction in the form \frac{a}{b} where a and b are integers.
    Hello Stevo

    I would first write

    0.454545454545 \cdots

    as

    45 \times 10^{-2} \  + \  45 \times 10^{-4} \ + \ 45 \times 10^{-6} \  + \  45 \times 10^{-8} \cdots

    \Rightarrow 45 ( 10^{-2} \  + \  10^{-4} \ + \ 10^{-6} \  + \  10^{-8} \cdots )

    Just find the sum of the infinite geometric series and simplify.

    Bobak
    Last edited by bobak; June 3rd 2008 at 02:39 AM.
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