Let the summation from k=1 to infinity of a_k be a nonabsolutely convergent series. Show that there is a rearrangement of this series so that the sequence of a partial sums of the rearranged series converges to infinity.
Also, show that there is a rearrangement of this series so that the sequence of partial sums of the rearranged series is bounded but does not converge.
Thanks!