# Math Help - rearranged series

1. ## rearranged series

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!

2. Originally Posted by friday616
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!
Since the series is not absolutely convergent (but presumably convergent) the sums of the sub-sequences of positive and negative terms must diverge.

CB