Re: infinite series
Conceptually is the best way to put it, because I don't think you would find it particularly illuminating for me to put it technically. The idea basically is this: as n gets huge, each additional term in the series is 1/3. So if X is the sum of the first 1000000 terms, X + 1 will be very close to the sum of the first 1000003 terms. Notice that no matter how many terms I pick, something like this will be true. So there's no limit to how big the sum gets, and so it doesn't converge.
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