Comparison Tests Lesson 9.4

Direct Comparison Test Given If converges, then converges What if What could you conclude about these?

Try It on These Test for convergence, divergence Make comparisons with a geometric series or p-series

Limit Comparison Test Given ak > 0 and bk > 0 for all sufficiently large k … and … =L where L is finite and positive Then either both converge … or both diverge

Limit Comparison Test Strategy for evaluating Find series with know convergence and general term "essentially same" Verify that this limit exists and is positive Now you know that behaves the same as

Example of Limit Comparison Convergent or divergent? Find a p-series which is similar Consider Now apply the comparison

Assignment Lesson 9.4 Page 628 Exercises 1 - 27 odd