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Ratio and Root Tests

Ratio and Root Tests. Thm . Ratio Test Let Ʃ a n be a series with nonzero terms. If , the series is abs. convergent. If , the series is divergent. If , then the test fails. Ex. Ex. Thm . Root Test Let Ʃ a n be a series.

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Ratio and Root Tests

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  1. Ratio and Root Tests • Thm.Ratio Test • Let Ʃan be a series with nonzero terms. • If , the series is abs. convergent. • If , the series is divergent. • If , then the test fails.

  2. Ex.

  3. Ex.

  4. Thm.Root Test • Let Ʃan be a series. • If , the series is abs. conv. • If , the series is divergent. • If , then the test fails.

  5. Ex.

  6. Ex.

  7. p. 781: 2, 3, 6, 13, 23, 27

  8. p. 784: 1, 3, 4, 5, 6, 8, 10, 12, 21, 26

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