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 Quote by HallsofIvy What's wrong with using the comparison test is that it only applies to positive series. Certainly -n< (1/2)n for all n, but we can't use that to conclude that $\sum -n$ converges! The crucial point is that every an is positive. That means that $\sum a_n x^n$, for x negative is an alternating series. What is true of alternating series?