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osanseviero

  • 2 years ago

Write the next series completly and write to what tends when you get the limit

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  1. osanseviero
    • 2 years ago
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    \[Sn=\frac{ 6 }{ 10 }+\frac{ 6 }{ 100 }+...\]

  2. anonymous
    • 2 years ago
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    is your job to add up \[\frac{6}{10}+\frac{6}{100}+\frac{6}{1000}+...\] which is the same as \[0.6666...\]

  3. anonymous
    • 2 years ago
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    you probably already know this one since \(0.33333...=\frac{1}{3}\) then if you double it you get \(0.6666...=\frac{2}{3}\)

  4. osanseviero
    • 2 years ago
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    Yep, I know that...so what should I do...keep adding?

  5. osanseviero
    • 2 years ago
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    oh....I see...it is 0.6666

  6. osanseviero
    • 2 years ago
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    So it tends to 0.66666... in infinity?

  7. osanseviero
    • 2 years ago
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    And how to write the complete series?

  8. anonymous
    • 2 years ago
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    \(\overline{.6}=\frac{2}{3}\)

  9. anonymous
    • 2 years ago
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    i was assuming you knew what "point six" repeating is if you have so sum a geometric series, we can do that as well, but you are still going to get \(\frac{2}{3}\)

  10. osanseviero
    • 2 years ago
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    I knew. So...its tendency and writing the series is the same?

  11. osanseviero
    • 2 years ago
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    Oh... \[Sn?\frac{ 6 }{ 10 }\times \frac{ 1 }{ 10 }^{n-1}\]

  12. osanseviero
    • 2 years ago
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    that is an =

  13. anonymous
    • 2 years ago
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    are you familiar with sigma notation?

  14. osanseviero
    • 2 years ago
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    Yep

  15. osanseviero
    • 2 years ago
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    so...

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