On the sum of the reciprocals of k-generalized Pell numbers

In this paper, we establish a formula for finding the closest integer to the reciprocal of S-m=n 1/P-m((k)) where {P-n((k)) }(n=-(k-2)) is the k-generalized Pell sequence or the k-Pell sequence given byP(n)((k)) = 2P( n-1) ((k))+ ... + P-n-k((k)) for all n = 2,with initial conditions P--(k-2)((k)) =P--(k-3)((k))= ...=P-0((k)) = 0 and P-1((k)) = 1. We show that the closest integer to the reciprocal of S-m=n 1/P-m((k)) is given by P-n((k)) - P n-1 ((k)) for every k = 2 and for every n = 2.