A Use for the Useless

themathkid:

Borwein integrals. Really, math? Really? 

Really.

One of my favourites is the Riemann series theorem and conditionally convergent series.

Let’s say you have a series:

This thing converges to ln(2), in the given order, but we can rearrange the terms, the exact same terms, and change the value it converges to. We can even make it diverge!

For example:

converges to ln(2)/2, half the previous value!

(via visualizingmath)