So I've seen that pi can be written as a series:

http://upload.wikimedia.org/math/4/b...be1ac3be60.png

$\displaystyle pi = 4 * series(((-1)^k)/2k+1)$

So pi = 4/1 - 4/3 + 4/5 - 4/7 + ...

Now I know thatQis an ordered field so ifaandbare inQ, if I add them, the resulta+bis another element inQ.

But if I sum up infinitely many rational numbers I can get an irrational? Wondering how this works.