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

Many sums do not converge to a finite value.

For 1+1/2+1/4…, it works. But most famously, 1+1/2+1/3+1/4… does not. This one keeps increasing to infinity.