In this paper, we prove some identities for the alternating sums of squares and cubes of the partial sum of the q-binomial coefficients. For example, we obtainOur proof leads to q-analogues of the sum of the first n squares and the sum of odd squares due to Schlosser. We also show that the q-binomial rational root theorem obtained by Slavin [Integers 8 (2008), #A05] can be easily deduced from the q-Lucas theorem.
|