\documentclass[a4paper]{article}
\begin{document}
\begin{eqnarray*}
y
 & = & \frac{x}{(a - x)^{2}} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
y
 & = & \frac{x}{(a - x)^{2}} \\
& = & \frac{x}{\left ( a \left ( 1 - \frac{x}{a} \right ) \right )^{2}} \\
& = & \frac{x}{a^{2} \left ( 1 - \frac{x}{a} \right )^{2}} \\
& = & \frac{1}{a^{2}} \frac{x}{\left ( 1 - \frac{x}{a} \right )^{2}} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
x
 & = & au \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
u
 & = & \frac{x}{a} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
y
 & = & \frac{1}{a^{2}} \frac{x}{\left ( 1 - \frac{x}{a} \right )^{2}} \\
& = & \frac{1}{a^{2}} \frac{au}{(1 - u)^{2}} \\
& = & \frac{1}{a} \frac{u}{(1 - u)^{2}} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
y
 & = & \frac{x}{(1 - x)^{2}} \\
& = & \sum_{n = 1}^{n = \infty} n x^{n} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
y
 & = & \frac{1}{a} \frac{u}{(1 + u)^{2}} \\
& = & \frac{1}{a} \sum_{n = 1}^{n = \infty} n u^{n} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
y
 & = & \frac{1}{a} \sum_{n = 1}^{n = \infty} n u^{n} \\
& = & \frac{1}{a} \sum_{n = 1}^{n = \infty} n \left ( \frac{x}{a} \right )^{n} \\
& = & \frac{x}{a} + 2 \left ( \frac{x}{a} \right )^{2} + 3 \left ( \frac{x}{a} \right )^{3} + 4 \left ( \frac{x}{a} \right )^{4}
 + 5 \left ( \frac{x}{a} \right )^{5} + \ldots \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\frac{\mbox{Term } (n + 1)}{\mbox{Term } (n)}
 & = & \frac{\frac{1}{a} (n + 1) \left ( \frac{x}{a} \right )^{n + 1}}{\frac{1}{a} n \left ( \frac{x}{a} \right )^{n}} \\
& = & \frac{(n + 1) \frac{x}{a}}{n} \\
& = & \frac{n + 1}{n} \frac{x}{a} \\
& = & \left ( 1 + \frac{1}{n} \right ) \frac{x}{a} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\lim_{n \to \infty} \left | \, \frac{\mbox{Term } (n + 1)}{\mbox{Term } (n)} \, \right |
 & < & 1 \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\lim_{n \to \infty} \left | \, \frac{\mbox{Term } (n + 1)}{\mbox{Term } (n)} \, \right |
 & = & \lim_{n \to \infty} \left | \, \left ( 1 + \frac{1}{n} \right ) \frac{x}{a} \, \right | \\
& \approx & \left | \, (1 + 0) \frac{x}{a} \, \right | \\
& = & \left | \, \frac{x}{a} \, \right | \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
y
 & = & \frac{1}{a} \sum_{n = 1}^{n = \infty} n \left ( \frac{x}{a} \right )^{n} \\
& & | \, x \, | \, \, < \, \, a \\
\end{eqnarray*}
\end{document}
