The Sum of Some (Infinite) Series Are Finite

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:

$$\sum_{n=0}^\infty ar^n = \frac{a}{1-r}$$

• $a$ is known as your “starting” amount
• $r$ is the “multiple” (remember, in a geometric series, each term is some “multiple” of the previous term)
  • $r$ 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 $r$ less than one

That’s kinda cool!