$\"\"$

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The series is $\"\"$ .

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Ratio test :

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Let $\"\"$ be a series with non zero terms.

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1. $\"\"$ converges absolutely if $\"\"$ .

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2. $\"\"$ diverges if $\"\"$ or $\"\"$ .

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3. The ratio test is inconclusive if $\"\"$ .

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

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$\"\"$

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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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Therefore series is convergent for all values of $\"\"$ .

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Radius of convergence is $\"\"$ .

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Interval of convergence is $\"\"$ .

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$\"\"$

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Radius of convergence is $\"\"$ .

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Interval of convergence is $\"\"$ .