They both get closer to but never reaching zero. Is the reason simply that one gets 1/x^2 gets closer to zero faster? So whats the threshold for something to be considered finite or infinite?
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This is equivalent to the reason why the sum of the harmonic series 1 + 1/2 + 1/3 + 1/4 + 1/5 … diverges, but the sum of the geometric series 1 + 1/2 + 1/4 + 1/8 … converges to 2. The reason for this was explained to me very intuitively: with the harmonic series, you can always find a finite number of subsequent terms in the series that are larger than the current term. With the geometric series I mentioned, that is not true.
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