#### Presentation Title

A Sum of Products Trick

#### Mentor

Vincent Ferlini

#### Location

David F. Putnam Science Center - 102

#### Abstract

Begin with any positive integer *n*. Write it as the sum of two smaller positive integers, say *a* and *b*. Compute the product *ab*. Repeat the same step in any order for each of the smaller numbers *a* and *b*. Continue this process until the only numbers left are 1s. Add up all the products. Regardless of the order in which the final 1s are obtained, the sum of the products will be the same. This talk will present the mathematics needed to explain why the products are the same and show how the ideas may be extended to other types of products whose sums will again be identical.

A Sum of Products Trick

David F. Putnam Science Center - 102

Begin with any positive integer *n*. Write it as the sum of two smaller positive integers, say *a* and *b*. Compute the product *ab*. Repeat the same step in any order for each of the smaller numbers *a* and *b*. Continue this process until the only numbers left are 1s. Add up all the products. Regardless of the order in which the final 1s are obtained, the sum of the products will be the same. This talk will present the mathematics needed to explain why the products are the same and show how the ideas may be extended to other types of products whose sums will again be identical.