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Math Help - can someone check this infinite geometric

  1. #1
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    can someone check this infinite geometric

    express the repeating decimal representaion of 1/9 as an infinite series using sigma notaion?

    so I will attach it and show you what I got!
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  2. #2
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    Quote Originally Posted by bobbluecow View Post
    express the repeating decimal representaion of 1/9 as an infinite series using sigma notaion?

    so I will attach it and show you what I got!
    The decimal is,
    .1111111111....
    Which is the convergent,
    \frac{1}{10}+\frac{1}{10^2}+...
    Thus,
    \frac{1}{10}\left(1+\frac{1}{10}+\frac{1}{10^2}+..  .\right)
    Thus,
    \frac{1}{10}\cdot \sum_{k=0}^{\mbox{ThePerfectHacker}}\frac{1}{10^k}
    If you want you can multiply in by the expression outside the sigma to get,
    \sum_{k=0}^{\mbox{ThePerfectHacker}} \frac{1}{10^{k+1}}

    Note,
    \mbox{ThePerfectHacker} represents \infty
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  3. #3
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    Hello, bobbluecow!

    Express the repeating decimal representaion of 1/9 as an infinite series using sigma notaion

    We have: . \frac{1}{9}\:=\:0.11111\hdots

    . . =\;0.1 + 0.01 + 0.001 + 0.0001 + \hdots

    . . =\;\frac{1}{10} + \frac{1}{10^2} + \frac{1}{10^3} + \frac{1}{10^4} + \hdots

    . . = \;\sum^{\infty}_{n=1}\frac{1}{10^n}

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