[AndrewC]

So you don't know what that little "sideways eight" atop the sigma symbol means? Sad.

It means you don't stop, not sad.

[edsheppa]

Oh, so you do know. Well that's more hopeful. But you think rational arithmetic is closed under that operation? Tell you what. Run this script, which as you can has nothing but rational arithmetic. I wonder if you will recognize the irrational number that is the limit. (Hint: it displeased a famous Greek.)

var x = 1
for (var i = 0; i < 1000; ++i)
{
    x = 1 + x;
    x = 1 / x;
    x = 7 * x;
    x = x / 4;
}
WScript.Echo(x + 1 / 2);