Help with comparison test and the last problem on practice exam

[belleamie]

Hey I have attach one of the practice exam that my professor gave out yrs ago as a study guide for our final. I think i need to use comparison for hte first two problems but have no clue where to start for the last one :(

 

[shmoe]

I don't believe 1) unless you assume $$\lim_{n\rightarrow\infty}na_n$$ exists. In this case, show that eventually $$a_n>L/n$$ where L is some fixed positive constant, and the result follows (comparison with harmonic series).

For 2) a straightforward comparison test will do- what have you tried?

For 3a) this should remind you of the usual proof that the harmonic series diverges, where you group the terms 1/3 and 1/4 together, 1/5 to 1/8 together, 1/9 to 1/16 together etc..

3b) shouldn't be a problem?

 

[dextercioby]

You know you're more than 3 years late with your homework :buggrin:

Daniel.