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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They don’t always, but there may be a limit to what they can equal, as eventually those fractions/decimals get so small that they become insignificant.
These are called geometric series, and if I recall it’s a Calculus I topic.
For your example, it does actually equal ~1 (well ~2, as you added a 1 to it) and there is a Wikipedia article with illustration:
https://en.wikipedia.org/wiki/1/2_%2B_1/4_%2B_1/8_%2B_1/16_%2B_%E2%8B%AF
Notice the language that the partial sum *tends* to 1, so not exactly; as yes, you end up adding something like 0.0000000000000000004 and next 0.0000000000000000002 and so on; but when we say that we go to infinity, then it’s 1.
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