On from Page 1 of these lecture notes it is stated in the final paragraph of the section titled CREW Mergesort:
Each such step (in a sequence of $\Theta(\log_2\ n)$ steps) takes time $\Theta(\log_2\ s)$ with a sequence length of $s$. Summing these, we obtain an overall run time of $\Theta((\log_2\ n)^2)$ for $n$ processors, which is not quite (but almost!) cost-optimal.
Can anyone show explicitly how the sum mentioned is calculated and the squared log result arrived at?