osanseviero
Write the next series completly and write to what tends when you get the limit
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osanseviero
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\[Sn=\frac{ 6 }{ 10 }+\frac{ 6 }{ 100 }+...\]
anonymous
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is your job to add up
\[\frac{6}{10}+\frac{6}{100}+\frac{6}{1000}+...\] which is the same as
\[0.6666...\]
anonymous
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you probably already know this one
since \(0.33333...=\frac{1}{3}\) then if you double it you get \(0.6666...=\frac{2}{3}\)
osanseviero
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Yep, I know that...so what should I do...keep adding?
osanseviero
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oh....I see...it is 0.6666
osanseviero
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So it tends to 0.66666... in infinity?
osanseviero
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And how to write the complete series?
anonymous
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\(\overline{.6}=\frac{2}{3}\)
anonymous
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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 \(\frac{2}{3}\)
osanseviero
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I knew. So...its tendency and writing the series is the same?
osanseviero
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Oh... \[Sn?\frac{ 6 }{ 10 }\times \frac{ 1 }{ 10 }^{n-1}\]
osanseviero
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that is an =
anonymous
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are you familiar with sigma notation?
osanseviero
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Yep
osanseviero
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so...