$\"\"$

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The function is $\"\"$ .

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(a)

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Find the geometric power series of the function

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$\"\"$

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$\"\"$

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The series is in the form of geometric series.

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The general form of geometric series is $\"\"$ .

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Substitute $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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The series is converges when $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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

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$\"\"$

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(b)

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Solve the series by long division method.

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The function is $\"\"$ .

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The series is $\"\"$ .

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$\"\"$

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$\"\"$

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