QuickSelect with Median of Medians runtime
The medians of medians algorithm will return a pivot with a rank between $\frac{3}{10}n$ and $\frac{7}{10}n$ in time $O(n)$.

You can then describe the worst-case computational complexity of Quickselect on an instance of $n$ elements with the following recurrence relation:
$$
T(n) = T\left(\frac{7}{10}n\right) + O(n),
$$
where $O(n)$ accounts both for the work needed to run the median-of-medians algorithm an for the partitioning of the input. 

Unrolling the recursion shows that (you can prove this formally by induction):
$$
T(n) \le c n \sum_{i=0}^{+\infty} \left( \frac{7}{10} \right)^i = cn \cdot  \frac{1}{1-\frac{7}{10}} = \frac{10cn}{3} = O(n),$$

where $c&gt;0$ is a suitable constant (hidden in the $O(n)$ notation of the recurrence relation).