Infinite series happen when we add up an endless list of numbers. These series can be grouped into two main types: convergence and divergence.

1. Convergence:

   • A series converges when the total gets closer to a specific number as we add more parts.
   • For example, the geometric series $\sum_{n=0}^{\infty} ar^n$ converges if the common ratio $|r| < 1$. This means as you keep adding, the sum settles toward a particular value.

2. Divergence:

   • A series diverges when it doesn’t settle down to any specific number.
   • An example is the harmonic series $\sum_{n=1}^{\infty} \frac{1}{n}$. This series keeps growing larger and never finds a limit.

3. Tests for Convergence:

   • There are different tests that help us figure out if a series converges or diverges. Some of these tests are:
     • Ratio Test
     • Root Test
     • Comparison Test

It’s important to understand convergence and divergence. This knowledge helps us evaluate infinite series more effectively.