Need help

0.9=9/10.

I think can be like this:

$0.999...=\frac{9}{10}+\frac{9}{100}+\frac{9}{1000}+...$

$0.999...=​​\frac{9}{10}+(\frac{9}{10})(\frac{1}{10})+(\frac{9}{10})(\frac{1}{10})^2+...$

Using infinite geometric series, with a=$\frac{9}{10}$ and r=$\frac{1}{10}$:

$0.999...=\frac{\frac{9}{10}}{(1-\frac{1}{10})}=\frac{9}{10}\times\frac{10}{9}=1$

Hope this help.