Rearrangements of divergent series (Q793920)

This paper concerns divergent series and the effects of rearrangements and the behaviour of convergent subseries on the rate of divergence. It is shown that under suitable conditions a divergent series of positive terms tending to zero can be rearranged to have any prescribed asymptotic behaviour (a divergence analogue of Riemann's rearrangement theorem for conditionally convergent series).