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?
In: 59
Yes, the difference is that 1/x² approaches zero faster.
If you make rectangles of width 1 under the curve of 1/x, you end up adding the areas 1/1 + 1/2 + 1/3 +… This sum diverges, but just barely. Pretty much any other curve that approaches zero any faster will have a smaller enough area that you can add up all the rectangles and get a finite number.
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