$\"\"$

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The series is $\"\"$ .

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Ratio test :

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(i) If $\"\"$ , then the series $\"\"$ is absolutely convergent.

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(ii) If $\"\"$ or $\"\"$ , then the series $\"\"$ is divergent.

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(iii) If $\"\"$ , then the ratio test is inconclusive.

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Here $\"\"$ and $\"\"$ .

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Find $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Interval of convergence is $\"\"$ .

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The series is convergence for all values of $\"\"$ and the radius of the convergence is half the width of the interval.

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Radius of convergence is $\"\"$ .

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$\"\"$

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Radius of convergence is $\"\"$ .

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Interval of convergence is $\"\"$ .