eli5 how does the sum of infinite terms turns to be a finite value

Question

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.

In: 248

Answer 1

Say you try to sweep a pile of dust into a dustpan, but there is still some on the ground. You sweep the smaller pile, but there is still some on the ground. Now let’s pretend the dust has no minimum size and you also aren’t allowed to just give up and say “good enough.” If there is always some dust left, you can continue the cycle infinitely despite starting with a finite pile of dust.