$\"\"$

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The function is $\"\"$ .

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Divide the numerator and denominator by $\"\"$ .

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$\"\"$

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Consider $\"\"$ .

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This is sum of infinite series with $\"\"$ and common ratio $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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Find the interval of convergence of $\"\"$ .

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The above series is a geometric series with common ratio $\"\"$ .

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Geometric series is convergent when common ratio $\"\"$ .

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Therefore, the series is convergent if $\"\"$

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$\"\"$

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Interval of convergence is $\"\"$ .

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$\"\"$

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Power series representation of the function is $\"\"$ and

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Interval of convergence is $\"\"$ .