$\"\"$

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Ratio Test :

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

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

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

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$\"\"$

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The series is $\"\"$ .

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$\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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If $\"\"$ then $\"\"$ .

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$\"\"$

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$\"\"$ .

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Since $\"\"$ , then the series is $\"\"$ is inconclusive.

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But, $\"\"$ , so the series diverges.

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Therefore, the series $\"\"$ diverges. \ \

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$\"\"$

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Series is diverges. \ \