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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.

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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.

• In Scilab