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The function is .
(a)
Find the geometric power series of the function.
.
The series is in the form of geometric series.
The general form of geometric series is .
Substitute and .
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The series is converges when .
.
Therefore, the power series is and is converges in the interval .
(b)
Solve the series by long division method.
The function is .
The series is .
The power series is and is converges in the interval .
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