On: Does 1+2+3+... Really Equal -1/12?

[jsprogrammer]

>That same argument gives you Zeno's paradox.

I believe Zeno's paradox is on the rationals, not integers.

>You can sum a pattern of numbers in O(1) time if you use logic instead of brute force.

There may be closed solutions for finite summation patterns, but infinite summation patterns of integers have no solution (by definition).