# 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.

**Q1: **

Let us consider .

Find a power series representation for .

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Find its radius of convergence.

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**Q2: **

Let us consider .

Find a power series representation for .

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Find its interval of convergence.

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**Q3: **

Consider .

Find a power series representation for .

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Find its interval of convergence.

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**Q5: **

Consider the function .

Find the power series for .

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Identify 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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**Q10: **

Consider the function .

Find the power series for .

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Identify its interval of convergence.

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