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Objective 1a: Direct Comparison Test
Objective 1a: Direct Comparison Test
You will be able to determine whether a series of positive terms converges or diverges by the Direct Comparison or Limit Comparison Tests
Direct Comparison Test
Direct Comparison Test
Let's say that the individual term in a given sequence are always smaller than the terms in some known sequence. If the series built from that known sequence converges, what conclusion can you make. Your answer to that question will form the basis of the Direct Comparison Test. Duration: 13:48
Comparing to a p-Series
Comparing to a p-Series
On Example 2, we have a series that resembles Σ(1/n²). You'll quickly discover, however, that we have difficulty establishing the necessary inequality required by the Direct Comparison Test. Perhaps we can amend our strategy before applying the test... Duration: 6:52
Comparing to a Geometric Series
Comparing to a Geometric Series
In the last couple of examples, we have been comparing our series to a know p-series. Let's look at two examples that compare more favorably to know geometric series. Duration: 11:00
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