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ABSTRACT. This paper develops the approach to the evaluation of a class of infinite series that involve special products of binomial type, generalized harmonic numbers of order 1 and rational functions. We give new summation results for certain infinite series of non-hypergeometric type. New formulas for the number π are included.

ABSTRACT. The aim of the paper is the investigation of special infinite series of the formand {f n (n)} n∈N 0 is a sequence of rational functions. A general summation method for the sum above in the case of the special choice of parameters a, b and f n (n) is included. We find the 2m-tuple of rational numbers α i , β j (1 ≤ i ≤ m, 1 ≤ j ≤ m) for which

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