18.
Given that \(p\) is a positive constant,
- show that
$$\sum _ { n = 1 } ^ { 11 } \ln \left( p ^ { n } \right) = k \ln p$$
where \(k\) is a constant to be found,
- show that
$$\sum _ { n = 1 } ^ { 11 } \ln \left( 8 p ^ { n } \right) = 33 \ln \left( 2 p ^ { 2 } \right)$$
- Hence find the set of values of \(p\) for which
$$\sum _ { n = 1 } ^ { 11 } \ln \left( 8 p ^ { n } \right) < 0$$
giving your answer in set notation.
\section*{Additional Answer Space }
\section*{Additional Answer Space }
\section*{Additional Answer Space }