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Radius of Convergence of a Power Series

Use the Ratio Test: lim_{n→∞} |a_{n+1}/a_n| = L. Converges absolutely if L<1; diverges if L>1; test inconclusive if L=1.

CalculusCommon Core LIM-8.CSERVerified correct ✓

Worked examples

Find the radius of convergence of the power series ∑_{n=1}^{∞} x^n / n. Use the ratio test: compute lim_{n→∞} |a_{n+1}/a_n|.
Answer: 1
Find the radius of convergence of the power series ∑_{n=0}^{∞} 4^n · x^n. Use the ratio test.
Answer: 0.25

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