[slevin063]

>For A1 and A2 to be equal, A2 will have limits x=1 to 5.

I should have added 'For A1 and A2 to be equal' at the start. If you want them to be equal, they need to have different limits and if they have same limits, they are not equal.

[ColinWright]

I'm finding that completely impossible to parse.

In particular:

    If you want them to be equal, they need
    to have different limits and if they have
    same limits, they are not equal.

That seems to be completely wrong. Consider these:

    sum_{x=0}^oo (-1)^x (1/x)

and

    sum_{y=0}^oo [ 1/(2y) - 1/(2y+1) ]

These are equal, and yet replacing the "oo" with n always gives partial sums that are different. So I guess I just don't understand what you are trying to say. Perhaps you could be more complete and explicit.