Given that \(p\) is a positive constant,
- show that
$$\sum_{n=1}^{11} \ln(p^n) = k \ln p$$
where \(k\) is a constant to be found, [2]
- show that
$$\sum_{n=1}^{11} \ln(8p^n) = 33\ln(2p^2)$$ [2]
- Hence find the set of values of \(p\) for which
$$\sum_{n=1}^{11} \ln(8p^n) < 0$$
giving your answer in set notation. [2]