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The Limit Comparison Test: Let k=1akand k=1bkbe two series with positive terms.

If limkakbk=L, where L is ___, then either the series both converge or both diverge.

If limkakbk=0and k=1bk___, then k=1ak___.

(There are two correct ways to fill in the last two blanks.)

Short Answer

Expert verified

Let k=1akand k=1bkbe two series with positive terms. If limkakbk=L, where L is a finite positive number, then either the series both converge or both diverge.

If limkakbk=0and role="math" localid="1649359537559" k=1bkconverges, then k=1akconverges.

Step by step solution

01

Step 1. Given Information

The given test is the limit comparison test.

02

Step 2. Explanation

  • If there are two series such that limkakbk=Lthen:
  • If L=0and k=1bkconverges, then k=1akalso converges.
  • If L=and k=1bkdiverges , then k=1akalso diverges.

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