TST Favor doctests over notebook testing

[drewejohnson]

I propose that we integrate tests into our documentation through doctests rather than rely on converting jupyter notebooks to python and then running them.
This has a few benefits:

1. We can ensure that our documentation is correct while we right the documentation - Sphinx guide on doctest extension
2. Once we move to pytest via ENH Transition to pytest for all testing #325, we can pick these up in the project testing and CI - pytest doctest integration
3. We can remove the need to keep and track the jupyter notebooks in the examples directory. These do provide some benefit, so we may want to move them somewhere, or figure out if we can generate a notebook from the documentation.

The main issue with keeping jupyter notebooks and example documentation is that we have to update both in the event of API changes. The notebooks are difficult to diff unless you use nbdime. I am open to keeping the notebooks, but then we have to make sure that, when there are API changes, both the documentation and the example notebooks get updated.