## osanseviero 2 years ago Write the next series completly and write to what tends when you get the limit

1. osanseviero

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

2. satellite73

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

3. satellite73

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

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

5. osanseviero

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

6. osanseviero

So it tends to 0.66666... in infinity?

7. osanseviero

And how to write the complete series?

8. satellite73

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

9. satellite73

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

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

11. osanseviero

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

12. osanseviero

that is an =

13. satellite73

are you familiar with sigma notation?

14. osanseviero

Yep

15. osanseviero

so...