New results on reciprocal series related to Fibonacci and Lucas numbers with subscripts in arithmetic progression

摘要

In this paper, we derive new expressions for some Fibonacci andLucas number related reciprocal series with subscripts in arithmeticprogression. We give expressions for both nite and in nite sums. Theresults, which we believe to be new, appear as special cases of somemore general series identities, which we prove to be true.