Step 1:

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The series is $\"\"$ , $\"\"$ .

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Find the interval of convergence using ratio test.

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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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Step 2:

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

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Find $\"\"$

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$\"\"$

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By the ratio test, the series is convergent when $\"\"$ .

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Therefore, interval of convergence is $\"\"$ , but need to check convergence at end points also.

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When $\"\"$ , then the series is $\"\"$ .

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$\"\"$

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Hence the series $\"\"$ is diverges at $\"\"$ .

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The interval of convergence is $\"\"$ .

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Solution:

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The interval of convergence is $\"\"$ .

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