Question

help...

Answer 1

They both pass the divergence test. It's been a while since I've done these, but I would try the ratio test next. I'll see if I can remember.

Answer 2

The ratio test almost always works.

Answer 3

Ahh, but for the first one, you'll probably want to use the root test.

Answer 4

For the root test, the infinite root of the first function, (n^2+1)^-1/2 is just 1. From Wikipedia, this means that it diverges, provided that it approaches the limit only from above. Since (n^2+1)^-1/2 will never give you negative y values, I believe you can say that it diverges--but I would double check something else. Usually, these are designed to be tested using a particular method. Which method are you working on? The integral test may be easier. I'm working on the second one now.

Answer 5

i tried with integral test, i got infinity so it diverges indeed. (: how about the 2nd qn?

Answer 6

Right. The root test doesn't help, so we could try the ratio test or the integral test. I quickly and informally did the ratio test, and it gave me 1. This is probably another integral test.

Answer 7

how do u integrate that?

Answer 8

I'm working on it; it looks like it's going to be u substititon first(might want to pick a different letter) and then integration by parts. Might want to look over your notes to see if there is an easier test.

Answer 9

It doesn't look integrable. Let me break out my list of integral tests.

Answer 10

can we compare it to 1/n? or it doesnt work that way

Answer 11

I mean divergence tests. Ahh, right, limit comparison test might work.

Answer 12

1/n doesn't work because we have a function in the numerator.

Answer 13

okay.. so what known function do we compare it with?

Answer 14

The second one is basically just the harmonic series which is just 1/1+1/2+1/3+1/4+... which we know diverges. By putting e^(1/n) on top which is always a number greater than 1, all that can possibly do is increase an already divergent series even more! So it must be divergent.

Answer 15

ahh. right. That's it! For some reason, when I redid the ratio test, I got that it can converge. I must have made a mistake--I'll check again.

Answer 16

so the method used is comparison test? yeah it makes alot of sense what kainui said.

Answer 17

Right, I dropped the fraction on the exponent when I did it just now. Very clever solution, @Kainui

Answer 18

thank you guys! :D

Answer 19

Yeah try to just "be real" with what you're looking at. Compare it to things you know already and it starts to become kind of obvious. like the first one, if you just imagine that +1 to be a 0 you'll see that THAT TOO is just the harmonic series as well! All they've done is simply add a 1 in a clever slightly different way that really doesn't fundamentally change it.