\documentclass{article}
\usepackage{amsmath}
\begin{document}
\paragraph{Sideset}
\[ \sideset{}{'}\sum_{i=1}^\infty S_i \]
\[  \sideset{_a}{_c}{\sum} x\]
\[  \sideset{^b}{^d}{\sum} x\]
\[  \sideset{_a}{^d}{\sum} x\]
\[  \sideset{^b}{_c}{\sum} x\]
\[  \sideset{_a^b}{_c^d}{\sum} x\]
\[  \sideset{^b_a}{^d_c}{\sum} x\]
\[  \sideset{{}_a{}^b}{{}_c{}^d}{\sum} x\]
\[  \sideset{{}^b{}_a}{{}^d{}_c}{\sum} x\]

\paragraph{Classic}
\[  {}_a^b\sum_c^d x\]
\[  {}^b_a\sum^d_c x\]
\[  {}_a^b\sum\nolimits_c^d x\]
\[  {}^b_a\sum\nolimits^d_c x\]
\[  {}_a{}^b\sum{}_c{}^d x\]
\[  {}^b{}_a\sum{}^d{}_c x\]

\paragraph{Multi}
% Cannot use multiple sub/supers!
%\[  \sideset{_a^b_c^d}{_e^f_g^h}{\sum} \]
%\[  \sideset{_a_c}{_e}{\sum} \]

\[  {}_a^b{}_c{}_d^e\sum\nolimits_f^g x\]
\[  {}_a^b{}_c{}_d^e\sum\nolimits_f^g{}_i{}_j^k x\]

% However, NOTE that the following `works'
% BUT, LaTeXML WILL WARN!!!!
\[  \sideset{u}{_ev}{\sum} x\]
\end{document}
