%0 Journal Article
%T Some Nice Sums are Almost as Nice if you turn them Upside Down
%A Moa Apagodu
%A Doron Zeilberger
%J Mathematics
%D 2009
%I arXiv
%X We represent the sums $\sum_{k=0}^{n-1}{n \choose k}^{-2}$, $\sum_{k=0}^m{m\choose k}^{-1}{a\choose n-k}^{-1}$, $\sum_{k=0}^{n-1}\frac{q^{-k(k-1)}}{{\genfrac{[}{]}{0pt}{}{n}{k}}_q}$, and the sum of the reciprocals of the summands in Dixon's identity, each as a product of an {\it indefinite hypergeometric sum} times a (closed form) {\it hypergeometric sequence}
%U http://arxiv.org/abs/0907.3174v2