Like the title says!
One concrete example is geometric series (but only when each term is some fraction of the previous).
Here’s the formula that dictates the resultant finite sum:
- is known as your “starting” amount
- is the “multiple” (remember, in a geometric series, each term is some “multiple” of the previous term)
- must be less than 1 in order for this sum to be finite (i.e. this formula assumes r less than 1!)
- so not all geometric series result in a finite sum, only ones with less than one
That’s kinda cool!