Question

I was helping one member today and I got the impression that he/she did not
know this method. Here is an explanation of that topics.

\[

.baaaaaaaa =\frac b {10^n}+\frac a {10^{m+n}}+\frac a {10^{m^2+n}}+
\frac a {10^{m^4+n}}+ \cdots =\\
\frac b {10^n}+\frac a {10^{m+n}}\left(1+\frac a {10^{m}}+
\frac a {10^{m^2}}+ \cdots \right)=\\
\frac b {10^n}+\frac a {10^{m+n}}\left(
\frac {1 }
{1- \frac a {10^{m}}
\right)\\


\]