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10.6 Comparison Tests for Convergence

1 min readjune 18, 2024


AP Calculus AB/BC ♾️

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Intro to the Comparison Tests

When you can’t use the integral test, you can see if the series looks like a geometric or p-series. From this, you can use these similarities to determine whether a series converges or diverges.

What is the Direct Comparison Test?

The Direct Comparison Test is as follows:
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https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(758).png?alt=media&token=c3c358fa-e71f-4ba9-aa16-fc65e6e70584

What is the Limit Comparison Test?

The Limit Comparison Test is as follows:
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(759).png?alt=media&token=9dfd56c4-0526-43e9-b6a9-5e1726e8a835
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(760).png?alt=media&token=0149c335-a837-4780-ae6f-73f434fa929d
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Problems

1. State the two comparison tests. What are the differences between them?
Determine whether the following series converge or diverge.
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