A Summation Formula for Sequences Involving Floor and Ceiling Functions
Michael A. Nyblom · Rocky Mountain Journal of Mathematics · 2006
A closed form expression for the N th partial sum of the pth powers of √ n is obtained, where • denotes the nearest integer function.As a consequence, a necessary and sufficient condition for the divisibility of n by √ n is derived together with a closed form expression for the least nonnegative residue of n modulo √ n .In addition an identity involving the zeta function ξ(s) and the infinite series