# Thread: can someone check this infinite geometric

1. ## can someone check this infinite geometric

express the repeating decimal representaion of 1/9 as an infinite series using sigma notaion?

so I will attach it and show you what I got!

2. Originally Posted by bobbluecow
express the repeating decimal representaion of 1/9 as an infinite series using sigma notaion?

so I will attach it and show you what I got!
The decimal is,
.1111111111....
Which is the convergent,
$\displaystyle \frac{1}{10}+\frac{1}{10^2}+...$
Thus,
$\displaystyle \frac{1}{10}\left(1+\frac{1}{10}+\frac{1}{10^2}+.. .\right)$
Thus,
$\displaystyle \frac{1}{10}\cdot \sum_{k=0}^{\mbox{ThePerfectHacker}}\frac{1}{10^k}$
If you want you can multiply in by the expression outside the sigma to get,
$\displaystyle \sum_{k=0}^{\mbox{ThePerfectHacker}} \frac{1}{10^{k+1}}$

Note,
$\displaystyle \mbox{ThePerfectHacker}$ represents $\displaystyle \infty$

3. Hello, bobbluecow!

Express the repeating decimal representaion of 1/9 as an infinite series using sigma notaion

We have: .$\displaystyle \frac{1}{9}\:=\:0.11111\hdots$

. . $\displaystyle =\;0.1 + 0.01 + 0.001 + 0.0001 + \hdots$

. . $\displaystyle =\;\frac{1}{10} + \frac{1}{10^2} + \frac{1}{10^3} + \frac{1}{10^4} + \hdots$

. . $\displaystyle = \;\sum^{\infty}_{n=1}\frac{1}{10^n}$