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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The eli5 is that if an infinite sum adds up to a finite value it’s because at every step in the sequence you add less than the difference between that value and what you’ve added up before. It doesn’t really depend on things being less than a specific number like 1, but it does imply that for any number you pick, an infinite number of terms in the series are going to be less than it. There are many ways to achieve this but the details of exactly determining if the sum is finite (the series converges) is [beyond eli5](https://en.wikipedia.org/wiki/Convergent_series#Convergence_tests). Simply decreasing terms aren’t enough: for example 1/2+1/3+1/4+1/5… doesn’t converge.
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