1. The Integral Test; p-Series
Lesson 9.3

2. Divergence Test Be careful not to confuse
Sequence of general terms { ak }
Sequence of partial sums { Sk }
We need the distinction for the divergence test If
Then must diverge
Note this only tells us about divergence. It says nothing about convergence

3. Convergence Criterion
Given a series
If { Sk } is bounded above
Then the series converges
Otherwise it diverges
Note
Often difficult to apply
Not easy to determine { Sk } is bounded above

4. The Integral Test Given ak = f(k) Then either k = 1, 2, …
f is positive, continuous, decreasing for x ≥ 1
Then either
both converge … or
both diverge

5. Try It Out
Given
Does it converge or diverge?
Consider

6. p-Series Definition p-Series test Converges if p > 1
A series of the form
Where p is a positive constant
p-Series test
Converges if p > 1
Diverges if 0 ≤ p ≤ 1

7. Try It Out
Given series
Use the p-series test to determine if it converges or diverges

8. Assignment
Lesson 9.3
Page 620
Exercises odd