3.8 Simplifying Polynomial Expressions

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3.8.1 Partial Fractions

The next is a flowchart for partial fraction expansions.

The partial fraction expansion for,

Consider the example below where the order of the numerator is larger than the denominator.

When the order of the denominator terms is greater than 1 it requires an expanded partial fraction form, as shown below.

We can solve the previous problem using the algebra technique.

3.8.2 Summation and Series

The notation is equivalent to assuming and are integers and . The index variable is an index often replaced with j, k, m, and n.

Operations on summations:

Some common summations:

for both real and complex .

for both real and complex . For , the summation does not converge.

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