I would appreciate any comments, typos, etc.

Update (March 16, 2011):

Presentation from: Georgia Southern q-Series conference, March 15. Here is a link.

Update (June 11, 2011): The paper is published by the Electronic J. of Combinatorics, Vol 18 (2), P13 44 pp. Download.

**Keywords:**

Telescoping, Fibonacci Numbers, Pell Numbers, Derangements, Hypergeometric Series, Fibonacci Polynomials, q-Fibonacci Numbers, q-Pell numbers, Basic Hypergeometric Series, q-series, Binomial Theorem, q-Binomial Theorem, Chu--Vandermonde sum, q-Chu--Vandermonde sum, Pfaff--Saalschutz sum, q-Pfaff--Saalschutz sum, q-Dougall summation, very-well-poised 6 phi 5 sum, Generalized Hypergeometric Series, WZ Method