Q: How to automatically size nested parenthesis?

I suggest you load the mleftright package, issue the directive \mleftright (to avoid the unwanted insertion of extra whitespace), and issue the instruction \delimitershortfall-1sp. That way, the auto-sized parentheses will grow in size automatically, even if the enclosed material isn't "tall".

\documentclass{article}
\delimitershortfall-1sp
\usepackage{mleftright}
\mleftright % make \left & \right behave like \mleft & \mright 
\begin{document}
\[
\left(\left\langle\left\{\left[\left(\left(a+b%
 \right)c\right)\right]\right\}\right\rangle\right)
\]
\end{document}

If you were to comment out the instruction \delimitershortfall-1sp, you'd get