Written by the Fiveable Content Team • Last updated September 2025
Verified for the 2026 exam
Verified for the 2026 exam•Written by the Fiveable Content Team • Last updated September 2025
Definition
A p-series is a series of the form Σ(1/n^p), where n starts from 1 and goes to infinity, and p is a positive constant. It converges if the value of p is greater than 1, and diverges if the value of p is less than or equal to 1.
Related terms
Converges: When a series converges, it means that its terms add up to a finite value as more terms are added. It's like pouring water into a cup until it reaches its maximum capacity without overflowing.
When a series diverges, it means that its terms do not add up to a finite value as more terms are added. It's like pouring water into an infinite hole - no matter how much water you pour, it will never fill up completely.
A geometric series is a special type of series where each term is obtained by multiplying the previous term by a common ratio. For example, 2 + 4 + 8 + 16 + ... is a geometric series with common ratio 2.