check out "only 1/3 of the positive integers are even" [ Ссылка ] ,

An infinite geometric series converges only if |r| is less than 1. When it diverges, things are a lot more fun!!!
And yes, this is usually done with 0 = 1-1+1-1+1-1+..., i.e. Grandi's series, but I like to attach a story to make teaching more fun. : )



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