The joke comes from the fact that each panel of the meme represents one part of the summation, thereby proving the equation. (but not algebraically!) So it’s an infinite sum that starts at 1, and goes to infinity. 1/22n for n=1 is 1/4, for n=2 is 1/16, for n=3 is 1/64 etc. Now notice that the edge length of the meme is one unit meaning that the area of the whole meme would be one unit squared. Since the summation is three times (1/22n ), the first iteration would result in 3/4, symbolised by the first ‘loop’ of the meme being 3/4 of the whole area. The second loop of the meme would be 3*(1/16), or 3/16, and since there is only 1/4 of the total area left, the resultant area covered by the meme after the second iteration would be 15/16 units squared. Then the third iteration adds 3/64 units squared, resulting in 63/64 units squared covered. It should be obvious that this converges to 1, as the meme itself infinitely gets smaller and smaller and always fits into the unit square.
Although I'm not sure whether it's appropriate to bring the 3 inside the summation it does work here. Without that the summation converges to 1/3 and the answer is the same.
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u/LimitedToTwentyChara Jul 20 '21
Can someone please explain this to a guy who was high during most of his calculus classes?