# Lesson Worksheet: Representing Rational Functions Using Power Series Mathematics • 12th Grade

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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• E

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• E

Q2:

Let us consider .

Find a power series representation for .

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Find its interval of convergence.

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• E

Q3:

Consider .

Find a power series representation for .

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Find its interval of convergence.

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• E

Q4:

Use a power series to represent .

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Q5:

Consider the function .

Find the power series for .

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• E

Identify its interval of convergence.

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• E

Q6:

Consider the function .

Find the power series for .

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• D
• E

Identify its interval of convergence.

• A
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• D
• E

Q7:

Consider the function with the center .

Find the power series for .

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• E

Q8:

Consider the function with the center .

Find the power series for .

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• E

Q9:

Consider the function with the center .

Find the power series for .

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• E

Q10:

Consider the function .

Find the power series for .

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• B
• C
• D
• E

Identify its interval of convergence.

• A
• B
• C
• D
• E