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12-4 Convergent and Divergent Series

12-4 Convergent and Divergent Series. Convergent Series : An infinite series that approaches a limit Divergent Series: An infinite series that does not approach a limit. Are the following series convergent or divergent? 1) 2)2 + 4 + 6 + 8 + 16+… 3) 10 + 8.5 + 7 + 5.5+….

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12-4 Convergent and Divergent Series

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  1. 12-4 Convergent and Divergent Series

  2. Convergent Series: An infinite series that approaches a limit Divergent Series: An infinite series that does not approach a limit

  3. Are the following series convergent or divergent? 1) 2)2 + 4 + 6 + 8 + 16+… 3) 10 + 8.5 + 7 + 5.5+…

  4. Ratio Test: When the series is neither arithmetic or geometric, you can use the ratio test to determine if the series is convergent/divergent. (must have all positive terms) Find = r. If r < 1, the series is convergent. If r > 1 the series is divergent.

  5. Use the ratio test to determine if the series is convergent or divergent. 4) 5)

  6. 6) 7) 1+

  7. Comparison test: A series is convergent if each term is less than or equal to than the values of the corresponding term of some convergent series A series is divergent if each term of the series is greater than or equal to the value of corresponding term of some divergent series.

  8. Use the comparison test to determine whether the following series are convergent or divergent: 8) 9)

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