osanseviero
  • osanseviero
Write the next series completly and write to what tends when you get the limit
Mathematics
chestercat
  • chestercat
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osanseviero
  • osanseviero
\[Sn=\frac{ 6 }{ 10 }+\frac{ 6 }{ 100 }+...\]
anonymous
  • anonymous
is your job to add up \[\frac{6}{10}+\frac{6}{100}+\frac{6}{1000}+...\] which is the same as \[0.6666...\]
anonymous
  • anonymous
you probably already know this one since \(0.33333...=\frac{1}{3}\) then if you double it you get \(0.6666...=\frac{2}{3}\)

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osanseviero
  • osanseviero
Yep, I know that...so what should I do...keep adding?
osanseviero
  • osanseviero
oh....I see...it is 0.6666
osanseviero
  • osanseviero
So it tends to 0.66666... in infinity?
osanseviero
  • osanseviero
And how to write the complete series?
anonymous
  • anonymous
\(\overline{.6}=\frac{2}{3}\)
anonymous
  • anonymous
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
  • osanseviero
I knew. So...its tendency and writing the series is the same?
osanseviero
  • osanseviero
Oh... \[Sn?\frac{ 6 }{ 10 }\times \frac{ 1 }{ 10 }^{n-1}\]
osanseviero
  • osanseviero
that is an =
anonymous
  • anonymous
are you familiar with sigma notation?
osanseviero
  • osanseviero
Yep
osanseviero
  • osanseviero
so...

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