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00 Determine the radius of convergence of the power series > (x – 2)". n=0 = i

00 Determine the radius of convergence of the power series > (x – 2)". n=0 = i

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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00 Determine the radius of convergence of the power series E(x – 2)". n=0 i
Transcribed Image Text:00 Determine the radius of convergence of the power series E(x – 2)". n=0 i
Expert Solution
Step 1

Use the ratio test to find the radius of convergence of the power series ∑n=0∞(x-2)n

Ratio test: Suppose we have the series ∑bn. Let L=limn→∞bn+1bn. Then, 

  • If L<1 , the series is absolutely convergent and hence convergent.
  • If L>1, the series is divergent.
  • If L=1, the series may be divergent, conditionally convergent or absolutely convergent.
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