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The MWE

\documentclass{article}
\usepackage{amsmath,mathtools}
\begin{document}
    \[
        \adjustlimits\lim_{x\rightarrow 1^-}\lim_{n\rightarrow\infty}\,\sum_{k=0}^n a_kx^k
        =\adjustlimits\lim_{n\rightarrow\infty}\lim_{x\rightarrow 1^-}\,\sum_{k=0}^n a_kx^k
    \]
\end{document}

renders the output

enter image description here

Although better than not using \adjustlimits, it is slightly annoying to see different baselines rendered for essentially the same expression---just permuted. I expect this happens because \adjustlimits eats things left to right and determines what spacing to use based on the last expression.

Is there a way to use \adjustlimits in this instance to create the same spacing between both limit expressions? Or am I stuck with manual spacing?

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