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Instructions and problems for a mathematics homework assignment focused on generating functions and related power series expansions. Students are expected to solve problems involving binomial and extended binomial theorems, geometric series, exponential series, and logarithmic series. Warm-up exercises are provided for practice, while graded problems cover various counting problems and manipulations of generalized binomial coefficients.
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In order to do these problems, you will need to know some standard power series expansions, in particular, those of the following functions (see the table on p. 440):
—Turn page for problems—
The following exercises are of the “plug in” variety; they simply test your knowledge of the appropriate concept or formula (such as a power series expansion). In contrast to some combinatorial problems that have come up in the past, these problems require very little (if any) serious thought, and you should be able to do them virtually in your sleep. To get the most benefit from these problems, try to do them under exam conditions, without resorting to notes or books. Of course you could look things up, but that would defeat the purpose of these problems. Problems marked by an asterisk (*) are particularly instructive, so make sure you can do those. All problems are from Section 6.4 (Generating functions).
All are from Section 6.4.