$\"\"$

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The series is $\"\"$ .

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Consider $\"\"$ .

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Hence $\"\"$ .

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Substitute the corresponding values in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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If the value of $\"\"$ then $\"\"$ .

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$\"\"$

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$\"\"$

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The series is converges if and only if the value $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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The series is $\"\"$ .

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When $\"\"$ the series $\"\"$ is diverges.

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When $\"\"$ then the alternating series $\"\"$ converges.

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The series is diverges at $\"\"$ and converges at $\"\"$ .

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Therefore, the series is converges in the interval $\"\"$ . $\"\"$

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The series is converges in the interval $\"\"$ .