Real Analysis - Radius of Convergence
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Apr29-08, 01:30 PM
What's wrong with using the comparison test is that it only applies to
series. Certainly -n< (1/2)
for all n, but we can't use that to conclude that [itex]\sum -n [/itex] converges!
The crucial point is that every a
is positive. That means that [itex]\sum a_n x^n[/itex], for x negative is an
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.