$\"\"$

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The function is $\"\"$ .

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Rewrite the function.

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$\"\"$

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Since $\"\"$ .

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$\"\"$

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Consider $\"\"$ .

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$\"\"$

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Find the value of $\"\"$ .

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Substitute the corresponding values.

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

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$\"\"$

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$\"\"$ .

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For $\"\"$ , the series diverges since the successive terms do not tend to zero as $\"\"$ .

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

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$\"\"$

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