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Sect. 9-6 Alternating Series

Sect. 9-6 Alternating Series . Alternating Series . A series whose terms are alternately positive and negative. If n starts at 1, then the first term is positive. If n starts at 1, then the first term is negative. Alternating Series Test for Convergence .

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Sect. 9-6 Alternating Series

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  1. Sect. 9-6 Alternating Series

  2. Alternating Series A series whose terms are alternately positive and negative If n starts at 1, then the first term is positive If n starts at 1, then the first term is negative

  3. Alternating Series Test for Convergence

  4. 1. Does converge or diverge?

  5. 2. Does converge or diverge?

  6. 3. Does converge or diverge?

  7. 4. Does converge or diverge?

  8. 5. Show that converges

  9. 6. Does converge or diverge

  10. We now have 3 tests for convergence/Divergence nthTerm Test for Divergence: If , then diverges. This test is inconclusive if Geom. Series Test: → diverges, → converges and Alternating Series Test for Convergence: converges if 1. for all n after a certain n (terms never increase in absolute value) 2.

  11. Home Work Page 639 # 11,19,23,27,31,89,91, 92,and 95 and worksheet 9-6

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