38th Austrian Mathematical Competition 2007
Source: 1st round
February 7, 2009
floor functionLaTeXalgebra unsolvedalgebra
Problem Statement
Let be a positive real number and a non-negative integer. Determine S\minus{}T, where
S\equal{} \sum_{k\equal{}\minus{}2n}^{2n\plus{}1} \frac{(k\minus{}1)^2}{a^{| \lfloor \frac{k}{2} \rfloor |}} and T\equal{} \sum_{k\equal{}\minus{}2n}^{2n\plus{}1} \frac{k^2}{a^{| \lfloor \frac{k}{2} \rfloor |}}