Question

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

Answer 1

\[Sn=\frac{ 6 }{ 10 }+\frac{ 6 }{ 100 }+...\]

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

So it tends to 0.66666... in infinity?

Answer 7

And how to write the complete series?

Answer 8

\(\overline{.6}=\frac{2}{3}\)

Answer 9

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 \(\frac{2}{3}\)

Answer 10

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

Answer 11

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

Answer 12

that is an =

Answer 13

are you familiar with sigma notation?

Answer 14

Yep

Answer 15

so...