9

9. [Maximum mark: 7]

The sum of the first $n$ terms of a geometric sequence is given by $S_n = \sum_{r=0}^{n-1} 5(\log_2 c)^r$.

(a) Given that $S_n$ converges, find the range of possible values of $c$. [3]

(b) In the case where $c = 1.5$, find the least value of $n$ such that $|S_\infty - S_n| < 0.1$. [4]