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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It doesn’t turn to a finite value. We assign the expression 1 + 1/2 + 1/4 + … some finite value based on what we think makes sense. In your case if you create a sequence out of each “partial sum” (the sum of first 1, 2, 3 terms etc) we get 1, 1.5, 1.75, … and we can then say this approaches 2.
The important thing to remember is that there are also other methods of assigning finite values to expressions like this, not just the one I give above.
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