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#! /usr/bin/perl
use warnings;
...
            unless $A ** $n == 1 + ($A - 1) * sum(map $A ** $_, 0 .. $
+n - 1)
    }
}

\documentclass{article}
\title{Summation Fulguration}
...
Q.E.D.
\end{prf}
\end{document}