In this demonstration, we're going to apply the techniques of the proof of Proposition 7.30 to actually finding a rearrangement of

which will converge to a given number.

Choose a real number in the box below, and press Enter. Then press the Next button in the next page repeatedly to see how the partial sums of the rearranged series are converging to the value you picked. Make sure that you can see, as the terms of the series evolve, that all the terms of the original sequence are popping up once, and once only.

Type a value for the rearranged series to converge to:

It probably isn't a good idea to pick numbers that are too big or too small (why?). Numbers between 0 and 2 give the best results.

Try a couple of numbers to see that you can get the partial sums converging to either one!

Return to the classMain page
Read the proof of Proposition 7.30

Analysis WebNotes by John Lindsay Orr.
Comments to the author: jorr@math.unl.edu

All contents copyright (C) 1996 John L. Orr
University of Nebraska--Lincoln
All rights reserved

Last modified: May 1996