View Single Post
Apr29-08, 01:30 PM
Sci Advisor
HW Helper
P: 25,235
Quote Quote by HallsofIvy View Post
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 [itex]\sum -n [/itex] converges!

The crucial point is that every an is positive. That means that [itex]\sum a_n x^n[/itex], for x negative is an alternating series. What is true of alternating series?
All of terms a_n*R^n are positive and it's convergent. The series is absolutely convergent. Nothing can go wrong here.