Answers and comments for Math 242 Homework 8.


#1a. Final answer is 0.

Can apply L'Hopital once.


#1b. Final answer is infinity (doesn't exist).

Can apply L'Hopital once, OR say it follows from #1a.


#2. Final answer is infinity (diverges).

Can use substitution: u = ln x.


#3. Diverges.

Constant times harmonic series.


#4. Diverges.

Using "pre-test", terms approach ln(1/2), not 0.


#5. Diverges.

Can use basic comparison. Terms are greater than 3^n/2^n.


#6. Converges.

Can use integral test, or perhaps basic comparison
(e.g. n/e^n < 2^n/e^n)


#7. Converges.

Can use integral test. Substitute u = ln x.


#8. Diverges.

Can use integral test. Can use result from #2.
Can also use basic comparison (e.g. ln n < 1)


#9. Converges.

Can use integral test (integrate by parts)
or basic comparison (e.g. ln n < n)