# can someone check this infinite geometric

• Oct 23rd 2006, 06:53 PM
bobbluecow
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!
• Oct 23rd 2006, 07:02 PM
ThePerfectHacker
Quote:

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,
$\frac{1}{10}+\frac{1}{10^2}+...$
Thus,
$\frac{1}{10}\left(1+\frac{1}{10}+\frac{1}{10^2}+.. .\right)$
Thus,
$\frac{1}{10}\cdot \sum_{k=0}^{\mbox{ThePerfectHacker}}\frac{1}{10^k}$
If you want you can multiply in by the expression outside the sigma to get,
$\sum_{k=0}^{\mbox{ThePerfectHacker}} \frac{1}{10^{k+1}}$

Note,
$\mbox{ThePerfectHacker}$ represents $\infty$
• Oct 23rd 2006, 09:44 PM
Soroban
Hello, bobbluecow!

Quote:

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

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

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

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

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