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Large partial random permutations of conditionally convergent series

This paper studies the behaviour of sums of series under random permutations. The first result considers the case of uniformly distributed permutations on the set N of all integers, which requires finitely additive probability. The next result considers the limit of the first portion p, , of a uniform distribution on the first n integers, as n gets large. The focal point is when , the permuted sum converge to a class of non-degenerate distributions which to the best of our knowledge is unknown in the literature. Finally, we address the question of when the limiting distribution has a continuous density, including the well known Erdös problem [3,9] as a special case.