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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If every term is 1 or more, then yeah, the sum will be infinite. The terms have to get smaller and smaller and/or sometimes be negative for the sum to finite (and even then it’s not guaranteed! 1 + 1/2 + 1/3 + 1/4 + 1/5 + … is infinite!).
For positive stuff it has to get small fast enough. Anything where you get the next term by multiplying by something between 0 and 1 shrinks fast enough (e.g. 1 + 99/100 + (99/100)^2 + … = 100).
It’s entirely possible for *some* of the terms to be > 1 and still have a finite sum. Just multiply everything by a constant, e.g. given that 1+1/2+1/4+… = 2 it should be obvious that 2+1+1/2+… = 4.
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