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Originally Posted by Dilbert1234567
i seem to recall that any convergent sum can actually converge to any number depending on how you organize the parts...
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Could you elaborate on your statement. Do you mean: any sum has a means of organization such that its sum can be found, or; the sum can be whatever I want it to be? The only example I can possibly think you are referencing is a sum that diverges due to oscillation:
s = 1 + -1 + 1 + -1 + 1 + -1 + . . .
This can be arranges two ways:
s = {1 + -1} + {1 + -1} + {1 + -1} + . . . = 0
s = 1 + {-1 + 1} + {-1 + 1} + {-1 + . . . = 1
Neither of those organizations is correct since the sum of that series is indeterminate due to the oscillation.