# 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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Q11:

Consider the power series representations of and . Use them, or otherwise, to calculate the first three nonzero terms, in ascending powers of , for the power series of .

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Q12:

Consider the power series . If , what is the radius of convergence of ?

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Q13:

Using partial fractions, calculate the power series of .

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Q14:

Consider the power series representations of and . Use them to calculate the first four nonzero terms, in ascending powers of , for the power series of .

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Q15:

Consider the power series and . Find the first three nonzero terms, in ascending powers of , of the power series that represents .

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Q16:

Consider the power series of . By calculating , calculate the first three nonzero terms, in ascending powers of , for the power series of .

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