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