Sumthing Strange

Maybe it's just the math geek in me, but I've always been fascinated by the following sum:
1 + 1/4 + 1/9 + 1/16 + 1/25 + 1/36 + 1/49 + 1/64 + ...... = (Pi * Pi) / 6

which is equal to:

I know this sum can be proven by complex analysis, but I've always thought there must be an easier proof. If I ever find it, you'll be the first to know.
To compute this sum yourself, enter the number of terms you would like to sum below and then hit the calculate button:
I've never been able to figure out how the Pi * Pi gets in there. If you have any further insight, drop me an e-mail. In fact, even if you don't give a hoot, drop me an e-mail anyway!