Infinite series are really important in higher-level math for a few reasons:

• Convergence: This means we can figure out if an infinite series gets closer to a certain number as we keep adding more and more terms.

• Functions: Infinite series can also show us how functions work, like $e^x$ or $\sin(x)$. This is super important in calculus and more advanced math.

• Real-World Applications: They help us understand things in physics and engineering. This connects math to things we see in everyday life.

In short, infinite series are valuable tools that help us learn more about math!