Find the binomial expansion of \(( 1 + 3 x ) ^ { - 1 }\) up to and including the term in \(x ^ { 2 }\)
9
(ii) Show that the first three terms in the binomial expansion of
$$\frac { 1 } { 2 - 3 x }$$
form a geometric sequence and state the common ratio.
9
It is given that
$$\frac { 36 x } { ( 1 + 3 x ) ( 2 - 3 x ) } \equiv \frac { P } { ( 2 - 3 x ) } + \frac { Q } { ( 1 + 3 x ) }$$
where \(P\) and \(Q\) are integers.
Find the value of \(P\) and the value of \(Q\)
9
Using your answers to parts (a) and (b), find the binomial expansion of
$$\frac { 12 x } { ( 1 + 3 x ) ( 2 - 3 x ) }$$
up to and including the term in \(x ^ { 2 }\) [0pt]
[2 marks]
9
(ii) Find the range of values of \(x\) for which the binomial expansion of
$$\frac { 12 x } { ( 1 + 3 x ) ( 2 - 3 x ) }$$
is valid.