http://upload.wikimedia.org/math/4/b/3/4b325f4142cab62b1786d8be1ac3be60.png

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

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

Now I know that

**Q**is an ordered field so if

**a**and

**b**are in

**Q**, if I add them, the result

**a+b**is another element in

**Q**.

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