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this post was submitted on 11 Sep 2024
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Written a bit more explicitly (although I kinda handwaved away the final term--the point is that you end up with one unpaired term which goes to zero)
edit: I was honestly confused about how exactly this related to the question, but seeing the comment from @yetAnotherUser@discuss.tchncs.de (not visible from Hexbear) which showed that the first sum in the image is equivalent to
the sum from n = 1 to ∞ of 2/(n * (n + 1))
made things clear (just take the above, put 2 in the numerator, and you get a result of 2)