If you re-arrange the terms, you can find that that series equals tau/4.
No, no you can't it's tau/8.
Its a conditionally convergent series; you can re-arrange the terms to add up to any real number you like (or diverge). [1].
You can construct a new series such that every term in the old one is there. However, if you try and rearrange the terms you end up with a backlog that coverages to the difference between the series. Which is why the actual series converges in the first place.
Re:The State of the Tau
by philthesong on Friday June 28, 2013 @05:01PM
(#5960319)
Does pi/4 equal to tau/8?
Re:The State of the Tau
by jessriedel on Friday June 28, 2013 @05:08PM
(#5960348)
Yes.
pi/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - ...