# 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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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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Q4:

Use a power series to represent .

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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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Q11:

Find a power series representation 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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