ERIC Number: EJ856229
Record Type: Journal
Publication Date: 2008-May
Abstractor: As Provided
Reference Count: 0
An Alternate Approach to Alternating Sums: A Method to DIE for
Benjamin, Arthur T.; Quinn, Jennifer J.
College Mathematics Journal, v39 n3 p191-202 May 2008
Positive sums count. Alternating sums match. Alternating sums of binomial coefficients, Fibonacci numbers, and other combinatorial quantities are analyzed using sign-reversing involutions. In particular, we describe the quantity being considered, match positive and negative terms through an Involution, and count the Exceptions to the matching rule (the method of D.I.E.). Careful use of this technique often results in nice generalizations. Any sum arising from the Principle of Inclusion-Exclusion (P.I.E.), such as the number of derangements, can be understood using D.I.E. too.
Descriptors: Numbers, Mathematics Instruction, College Mathematics, Problem Solving, Generalization, Mathematical Logic
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education
Authoring Institution: N/A