Question

Test for convergence or divergence.
1/(n^(1+1/n))
I have no idea where to start with this one..

Answer 1

Is it
\[
\frac {1}
{n^{1+\frac 1 n}}
\]

Answer 2

yes thats correct

Answer 3

I am not sure which method to use here. I was thinking comparison test, but what would i campare it to?

Answer 4

Whoops, took me a sec for the light bulb to click. You have to use the fact that when you multiply exponents that have a common base, the exponents simply get added. The denominator can be rewritten as n^(1)*n^(1/n)

Answer 5

so could i use the comparison test and use (1/n) and compare it to the whole thing?

Answer 6

That might work, yes. Either way, I would try comparison series as well at first glance.

Answer 7

Well, wait, just choose 1/n^2, since its a convergent p-series.

Answer 8

so i would compare 1/n^2 to the whole thing?

Answer 9

You can, definitely.

Answer 10

Use the limit comparison test to see that it is divergent

Answer 11

\[
\lim_{n->\infty}
\frac {\frac{1}{n \ n^{1/n}}}

{\frac 1 n}=\frac {1}{n^{1/n}}=1

\]

Answer 12

Your series behave like
\[
\frac 1 n
\]
which diverges.

Answer 13

that makes more sense now...thanks Eliass

Answer 14

YW

Answer 15

Then may I ask what is wrong with using the direct comparison test and using 1/n^2 as a comparison? Just to make sure of why I am wrong.

Answer 16

TO prove that is divergent you have to say that the n-th term is bigger than a divergent series.
1/n^2 is convergent.

Answer 17

I have to go to go to an appointment. Enjoy

Answer 18

Alrighty, have fun.

Answer 19

thanks for your input too Psymon...its appreciated :)

Answer 20

Just to say, I was trying to prove convergence, not divergence. I used the p-series and saw that the original series was less than my p-series for all n. Maybe I'm missing something, but who knows o.o

Answer 21

Who knows......and the battle continues :P

Answer 22

Fair enough. I remember when I was doing these I would forget whether the proof involved using another series or another limit. I would get the proofs mixed up and sometimes prove that a limit existed when I wanted to prove convergence instead. Oh well. You get through this part and you're good. This was honestly the most confusing partof calc II when i did it :P

Answer 23

Im trying to make it through....only 3 more weekd sof this class

Answer 24

Yeah, you're at the end for sure. Do you need calc III, differential, or any of that stuff?

Answer 25

i need both.

Answer 26

Gotcha. I'm taking differential and discrete math in a month. The website that linked me to openstudy in the first place is where I've been trying to preview D.Es. Might be worth a look.

http://tutorial.math.lamar.edu/Classes/DE/DE.aspx

Answer 27

It has calc III on there as well, but I have to wait for the spring for that because of schedule conflict :/

Answer 28

oh ok..ill check it out

Answer 29

: )