The Sum of all the values of 1/(n^2) where N > 0

A friend got the value: (pi^2)/6

I made a PHP program to test that.

http://lappy.heliohost.org/problem.php

How would you guys solve this problem?

You mean the sum of the range of the inverse square function? It's infinity. Duh.

No, it doesn't reach infinity. The limit is (pi^2)/6

If you run my program, you will see that hte program caculates around there.

The range of the inverse square function is common knowledge to be (0, infinity). As in, you can get as small as zero, and as large as infinity (as x nears zero, y nears infinity). Any addition of numbers containing infinity is infinity. Therefore, the sum of all possible y-values of the inverse square function is infinity.

I really don't see any practical purpose is calculating the sum of all possible ranges for a function...

EDIT
PS, if you put in .00000001 as x (just as an example), f(x) where f is the inverse square function is 10^16, which is way bigger than (pi^2)/6.

Lappy, that program has to be processor intensive... Does it loop forever?

Sorry, I meant all integral values.

Yes, it loops for a while; the PHP parser cuts it off (and it is set to run at a max of 2% of the processor power)

lol integral values might have helped