does this apply only for terms that are less than 1 eg 1 + 1/2 + 1/4…. or does this apply to all ap/gp. I remember studying this, but it’s been so long I remember only the gist.
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Walk halfway across the room. Walk half of what’s left. Walk half of what’s left. Keep doing that. You’ll get close to the other side of the room, you won’t travel an infinite distance.
If you view it in reverse, you can take a finite amount and slice it into an infinite number of parts using some rule or pattern. Adding up those parts just gives you the finite amount again.
But that’s only true for some infinite series that they add up to something finite. If an infinite series “converges”, it adds up to a finite number. If it “diverges”, then it adds up to infinity. You can show that it converges if every term is smaller than another infinite series that you know converges. Likewise, you can show it diverges if every term is larger than another infinite series that you know diverges.
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