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

Someone showed me this and it made it make sense.
The thought is “if I and an infinite number of things, no matter how small, an infinite number of times it should reach infinity.

So let’s start with the number .9

Let’s add .08=.98
Then .007=.987
.9876
.98765
.987654
.9876543
.98765432
.987654321
.9876543219
.98765432198
Etc

Do this forever! The answer will never reach infinity.

*edit
Dang, I don’t know how to make it to keep my formatting. it looks way cooler when the numbers make a little pyramid