Abstract
The aim of this research note is to provide the sums of the series $$\sum_{k=0}^{\infty}(-1)^k\({{a-i}\atop{k}}\)\frac{1}{2^k(a+k+1)}$$ for $i$ = 0, ${\pm}1$,${\pm}2$,${\pm}3$,${\pm}4$,${\pm}5$. The results are obtained with the help of generalization of Bailey's summation theorem on the sum of a $_2F_1$ obtained earlier by Lavoie et al.. Several interesting results including those obtained earlier by Srivastava, Vowe and Seiffert, follow special cases of our main findings. The results derived in this research note are simple, interesting, easily established and (potentially) useful.
