Comparison Tests

1
Comparison Tests

• Lesson 8.4

2
Direct Comparison Test

• Given
• If converges, then converges
• What if
• What could you conclude about these?

3
Try It on These

• Test for convergence, divergence
• Make comparisons with a geometric series or
  p-series

4
Limit Comparison Test

• Given ak gt 0 and bk gt 0 for all sufficiently
  large k and
• where L is finite and positive
• Then either both converge or both diverge

5
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

6
Example of Limit Comparison

• Convergent or divergent?
• Find a p-series which is similar
• Consider
• Now apply the comparison

7
Assignment

• Lesson 9.4
• Page 628
• Exercises 1 - 27 odd