$\"\"$

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The power series is $\"\"$ .

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Let $\"\"$ .

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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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$\"\"$

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

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$\"\"$

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

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Test for convergence at the boundaries.

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For $\"\"$ , $\"\"$

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$\"\"$ is divergent by $\"\"$ -series test.

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For $\"\"$ , $\"\"$

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$\"\"$ is convergent by alternating series test.

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

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$\"\"$

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Interval of convergence is $\"\"$ .