Extremal Problems for Numerical Series

In this paper, we consider extremal problems for numerical positive series. The terms of these series are pairwise products of the elements of two sequences, one of which is fixed and the other varies within a given set of sequences. We obtain exact solutions for a number of such problems. As one of the possible applications of the results obtained, we find solutions of some extremal problems related to best $n$-term approximations of periodic functions.