Infinite Processes

Sequences and series introduce you to the world of infinity! A sequence is just a list of numbers in a specific order, while a series is what you get when you add those numbers together.

Types of Series

• Geometric Series: Each term is multiplied by a constant to get the next.
• Telescoping Series: Many terms cancel each other.
• p-Series: Series of the form \( \sum \frac{1}{n^p} \).

Convergence and Divergence

Not all series add up to a finite number. Learning to test for convergence (like the Ratio Test or the Alternating Series Test) is key.

Where You'll See This

• Calculating interest in finance
• Modeling populations
• Approximating functions with polynomials