Series

Definition

A series is the sum of the terms of a sequence. In math, it often involves summing an infinite number of terms based on a specific rule or formula.

5 Must Know Facts For Your Next Test

1. The sum of a series can be finite or infinite depending on the sequence involved.
2. A geometric series has terms that form a constant ratio between successive terms.
3. An arithmetic series has terms that have a constant difference between consecutive elements.
4. The convergence or divergence of a series determines whether its sum approaches a finite value or not.
5. A partial sum represents the sum of the first n terms in a series.

Review Questions

• What distinguishes an arithmetic series from a geometric series?
• How do you determine if a series converges or diverges?
• What is meant by the term 'partial sum' in relation to a series?

Related terms

Sequence: An ordered list of numbers where each number is called a term.

Convergence: When the sum of an infinite series approaches a specific finite value as more terms are added.

Divergence: When the sum of an infinite series does not approach any finite limit as more terms are added.