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Thread: Applications of infinite geometric series

  1. #1
    Junior Member
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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 $\displaystyle 0.454545454545 \cdots$ as a fraction in the form $\displaystyle \frac{a}{b}$ where $\displaystyle a$ and $\displaystyle b$ are integers.
    Hello Stevo

    I would first write

    $\displaystyle 0.454545454545 \cdots$

    as

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

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

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

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