Ratio Test for Convergence
Abigail Young
6 min read
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Study Guide Overview
This study guide covers the Ratio Test for convergence of series in AP Calculus BC. It explains how to apply the test, focusing on series with exponentials and factorials. Several examples are provided to demonstrate how to determine if a series converges, diverges, or if the test is inconclusive. The guide also briefly reviews other convergence tests covered in Unit 10, including the nth term, integral, p-series, direct comparison, limit comparison, and alternating series tests.
#10.8 Ratio Test for Convergence
Welcome back to AP Calculus BC! Indeed, there are many tests that you have learned from this unit, and we are headed to the final one, the ratio test, which is useful for series with exponentials or factorials. 👆
#🤔 What is the Ratio Test?
In the bigger picture, a ratio relates two numbers and is represented as a quotient. If there are 4 apples and 3 oranges in a basket, we can also say that the basket has a 4:3 apple-to-orange ratio. 🍎
The Ratio Test works as follows:
Like all the other tests, this theorem will make more sense as we move through example problems. Without further ado, let’s dive right in!
#✏️ Ratio Test for...
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