# Worksheet: Operations on Power Series

In this worksheet, we will practice adding, subtracting, and multiplying two power series and finding the radius of convergence of the resulting power series.

**Q1: **

Suppose that is a power series whose interval of convergence is and that is a power series whose interval of convergence is .

Find the interval of convergence of the series .

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Find the interval of convergence of the series .

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**Q2: **

Use partial fractions to find the power series of the function .

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**Q3: **

Consider the power series .

Find the function represented by this series.

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Determine the interval of convergence of the series.

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**Q4: **

Consider the functions and .

Find the power series of .

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Find the power series of .

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**Q5: **

Let .

Construct a power series for the function .

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Find the interval of convergence of the power series.

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**Q6: **

Use partial fractions to find the power series of the function .

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**Q7: **

Consider the functions and .

Find the power series of .

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Find the power series of .

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**Q8: **

Multiply the series by itself to construct a series for . Write the answer in sigma notation.

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**Q9: **

Consider the power series .

Find the function represented by this series.

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Determine the interval of convergence of the series.

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Let . Find in sigma notation.

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**Q10: **

Find .

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