## osanseviero Group Title Write the next series completly and write to what tends when you get the limit 9 months ago 9 months ago

1. osanseviero Group Title

$Sn=\frac{ 6 }{ 10 }+\frac{ 6 }{ 100 }+...$

2. satellite73 Group Title

is your job to add up $\frac{6}{10}+\frac{6}{100}+\frac{6}{1000}+...$ which is the same as $0.6666...$

3. satellite73 Group Title

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 Group Title

Yep, I know that...so what should I do...keep adding?

5. osanseviero Group Title

oh....I see...it is 0.6666

6. osanseviero Group Title

So it tends to 0.66666... in infinity?

7. osanseviero Group Title

And how to write the complete series?

8. satellite73 Group Title

$$\overline{.6}=\frac{2}{3}$$

9. satellite73 Group Title

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 Group Title

I knew. So...its tendency and writing the series is the same?

11. osanseviero Group Title

Oh... $Sn?\frac{ 6 }{ 10 }\times \frac{ 1 }{ 10 }^{n-1}$

12. osanseviero Group Title

that is an =

13. satellite73 Group Title

are you familiar with sigma notation?

14. osanseviero Group Title

Yep

15. osanseviero Group Title

so...