Convergence Tests

[NaN-Gram]

I wanted some help with 31, 33, 37, and 43. These are the hardest problems of this chapter that I have had to deal with by far, but the problems that I didn't mention outright are ones that I have dealt with. I don't know how to deal with logarithms in cases like these, no e to exponents of n. I need some help to move forward.

 

[pka]

Question for NaN-Gram: Why are you asking us to read a sidways post?

 

[Steven G]

31 is a simple p-series. We know or should know that the ln function is an increasing function, that ln(1)= 0, ln(e) = 1 and that 1 < 2 < e. The answer immediately follows from the p-series test.
Don't be afraid of ln. Besides ln(2) is just a number as much as 17 is a number.

 

[Steven G]

33 is just screaming at you to use a certain test. Which test is it? Same for 37 and 43.

 

[NaN-Gram]

Question for NaN-Gram: Why are you asking us to read a sidways post?

I had trouble rotating the post, but I figured out how to fix it after I posted it. Sorry about that, I'll try not to do that again.