# Worksheet: Representing Rational Functions Using Power Series

In this worksheet, we will practice using the formula of the infinite sum of geometric series to find a power series representation for some rational functions.

**Q3: **

Consider .

Find a power series representation for .

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Find its interval of convergence.

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**Q6: **

Consider the function .

Find the power series for .

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Identify its interval of convergence.

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**Q7: **

Consider the function with the center .

Find the power series for .

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**Q8: **

Consider the function with the center .

Find the power series for .

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**Q9: **

Consider the function with the center .

Find the power series for .

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**Q12: **

Find a power series representation for .

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**Q13: **

Determine the interval of convergence for the power series of the function .

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**Q14: **

Find a power series representation for , centered at .

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**Q15: **

Write the first four terms of the power series of the function .

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