Rational combinations for the sums involving inverse binomial coefficients

We say that the number r can be expressed as a rational combination of the set T = {f(i)|i is an element of I} if there exist rational numbers d(i) such that r - Sigma(i is an element of J)d(i)f(i). In this paper, we study rational combinations for sums involving inverse binomial coefficients of the form: Sigma(n)(n >= 0)(pn+kqn)(-1) x(n), (x is an element of Q) where p; q; k is an element of N(0) and {a(n)} is any rational sequence. In several interesting cases of the sum, we obtain closed forms, recursion formulas and experimental results. (C) 2011 Elsevier Inc. All rights reserved.