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The root test states that

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(1) If then the series converges absolutely.

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(2) If  then the series diverges.

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(3) If and the limit approaches strictly from above then the series diverges.

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(4) Otherwise the test is inconclusive (the series may diverge, converge absolutely or

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converge conditionally).

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Now find the radius of convergence of the power series :

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Let then .

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Therefore it is convergent for therefore for it is convergent of .

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The radius of convergence of the power series is .

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