Master theorem can solve common divide-and-conquer recurrences.
Master Theorem
Recurrence: T(n) = aT($\frac{n}{b}$) + f(n).
$$
T(n)=\begin{cases}
\Theta(n^{log_b a}) & f(n)=\Omicron(n^c) & c < \log_b a \
\Theta(n^c log^{k+1} n) & f(n)=\Theta(n^c log^k n) & c = \log_b a \
\Theta(f(n)) & f(n)=\Omega(n^c) & c > \log_b a
\end{cases}
$$