The Integral Test; p-Series Lesson 9.3

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

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

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

Try It Out Given Does it converge or diverge? Consider

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

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

Assignment Lesson 9.3 Page 620 Exercises 1 - 35odd