\BOOKMARK [1][-]{section.1}{Introduction}{}% 1
\BOOKMARK [1][-]{section.2}{Background}{}% 2
\BOOKMARK [1][-]{section.3}{Proof of Theorem 2}{}% 3
\BOOKMARK [1][-]{section.4}{Proof of Theorem 3}{}% 4
\BOOKMARK [1][-]{section.5}{How Does This Method Work?}{}% 5
\BOOKMARK [1][-]{section.6}{Two applications for non-negative sums}{}% 6
\BOOKMARK [1][-]{section.7}{Details of Theorem 6}{}% 7
\BOOKMARK [2][-]{subsection.7.1}{Motivation}{section.7}% 8
\BOOKMARK [2][-]{subsection.7.2}{Proof of Lemma 4}{section.7}% 9
\BOOKMARK [2][-]{subsection.7.3}{Proof of Lemma 5}{section.7}% 10
\BOOKMARK [2][-]{subsection.7.4}{Proof of Theorem 6}{section.7}% 11
\BOOKMARK [2][-]{subsection.7.5}{Proof of Corollary 7}{section.7}% 12
\BOOKMARK [1][-]{section.8}{The third application for the alternating sum}{}% 13
\BOOKMARK [1][-]{section.9}{Acknowledgments}{}% 14