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Jan 1, 2019 at 16:13 comment added Steven Gubkin I like to ask about both the area and perimeter of the Koch snowflake as a first introduction to infinite series. The area converges, but the perimeter diverges. I usually need to show them the trick for summing a geometric series, but it makes for a fun ~hour long class activity.
Apr 2, 2014 at 21:14 comment added Brendan W. Sullivan I think the Sierpinski triangle is another good example to use and might even be (slightly) better since the "border" of the figure is fixed, and the area at any iteration is obviously a sum of triangular areas.
Apr 2, 2014 at 20:40 history edited Markus Klein CC BY-SA 3.0
important "not" was missing
Apr 2, 2014 at 20:27 history answered Markus Klein CC BY-SA 3.0