1. 9.4 Day 2 Limit Comparison Test

2. Limit Comparison Test If and for all (N a positive integer)
If , then both and
converge or both diverge.
If , then converges if converges.
If , then diverges if diverges.

3. Example 3a:
When n is large, the function behaves like:
harmonic series
Since diverges, the series diverges.

4. Example 3b:
When n is large, the function behaves like:
geometric series
Since converges, the series converges.

5. Use the limit comparison test to see if the series converges

6. Use the limit comparison test to see if the series converges
Compare to
This series converges
It is a p-series
Therefore the two series have the same growth rate.
They both converge

7. Tests we know so far: Try this test first
nth term test (for divergence only)
Then try these
Special series:
Geometric, P series, Telescoping
General tests:
Direct comparison test,
Limit comparison test,
Integral test,
Absolute convergence test (to be used with another test)

8. Homework p odd all
Mother: Does your teacher like you ?
Son: Like me, she loves me. Look at all those Xs on my test paper !
Q: What did one math book say to the other?
A: Man I got a lot of problems!