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Chapter 10: Q. 0 (page 777)

Read the section and make your own summary of the material.

Short Answer

Expert verified

The summary of the material is as follows.

Step by step solution

01

Step 1. Definition of Comparison Tests

  • Analyze series by comparing them with series whose behavior we understand.
  • Use inequalities to compare series.
  • Use limits to compare series.
02

Step 2. Summary of the section 

Comparison Test:

If 鈭�ann=1鈭�and 鈭�bnn=1鈭�are series with non-negative terms, then:

  1. If 鈭�bnn=1鈭�converges and an鈮�bnfor all n, then 鈭�ann=1鈭�converges.
  2. If 鈭�bnn=1鈭�diverges and an鈮�bnfor all n, then 鈭�ann=1鈭�diverges.

Limit Comparison Test

Let 鈭�ann=1鈭�and 鈭�bnn=1鈭�be positive-termed series. If

limn鈫�鈭�anbn=c,

where cis finite, and c>0, then either both series converge or both diverge.

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