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Unit 10

10.6 Comparison Tests for Convergence

1 min readโ€ขjune 8, 2020

peter-cao

Peter Cao


https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(565).png?alt=media&token=c9b56758-c8bf-40c4-8a4f-0522d9a8a009

Intro to the Comparison Tests

When you canโ€™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:
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(756).png?alt=media&token=858be3e7-e27b-4d51-bee4-6478d3bfa2f2
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(757).png?alt=media&token=f6e51a1e-607b-4536-ad55-372fe3b9e337
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
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(761).png?alt=media&token=b89aa76b-0ad0-4dfa-a3d2-7c858e0beac0

Problems

1. State the two comparison tests. What are the differences between them?
Determine whether the following series converge or diverge.
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(762).png?alt=media&token=280ebc70-8df0-4989-ab0a-5027bee92c28

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