7. (a) Write down the Maclaurin series expansion for \(\ln ( 1 - x )\) as far as the term in \(x ^ { 3 }\).
(b) Show that \(- 2 \ln \left( \frac { 1 - x } { ( 1 + x ) ^ { 2 } } \right)\) can be expressed in the form \(a x + b x ^ { 2 } + c x ^ { 3 } + \ldots\), where \(a , b , c\) are integers whose values are to be determined.