Explain $\log_2(n)$ squared asymptotic run-time for naive nested parallel CREW PRAM mergesort
You want to compute this sum:
$$
\sum_{i=1}^{\mathrm{log}\left( n\right) }\mathrm{log}\left( \frac{n}{{2}^{i}}\right)
$$

This can be easily rewritten to:
$$
\sum_{i=1}^{\mathrm{log}\left( n\right) }\mathrm{log}\left( n\right) - \sum_{i=1}^{\mathrm{log}\left( n\right) }i
$$

The first term is clearly $(\log(n))^2$. The second term is $(\log(n))^2/2+o((\log(n))^2)$. Summed, the result is $\Theta((\log(n))^2)$.