---
title: "Diverges — AP Calculus Definition & Exam Guide"
description: "Diverges means a limit, improper integral, or infinite series fails to approach a finite value. Essential for AP Calc Topics 6.13, 10.4, and 10.7 convergence tests."
canonical: "https://fiveable.me/ap-calc/key-terms/diverges"
type: "key-term"
subject: "AP Calculus AB/BC"
---

# Diverges — AP Calculus Definition & Exam Guide

## Definition

When a series or sequence diverges, it means that the terms of the series or sequence do not approach a finite value as the number of terms increases. In other words, the sum or limit of the terms does not exist.

## Related Study Guides

- [10.4 Integral Test for Convergence](/ap-calc/unit-10-infinite-sequences-and-series-bc-only-/integral-test-for-convergence/study-guide/KrBj7QZJaHcPOKsThiS2)

## Review

### Related Terms

- Converges: When a series or sequence converges, it means that the terms of the series or sequence approach a finite value as the number of terms increases. The sum or limit exists.
- [Infinite Series](/ap-calc/key-terms/infinite-series): An infinite series is an expression consisting of an infinite number of terms added together.
- [Geometric Series](/ap-calc/key-terms/geometric-series): A geometric series is a specific type of infinite series where each term is obtained by multiplying the previous term by a constant ratio.