# converge or diverge

1. ### converge/conditionally converge/diverge????

determine whether the series is absolutely convergent, conditionally convergent, or divergent. $\sum_{n=1}^{\infty} (\frac{n^2+2}{3n^2+2})^n$ how to do this problem?? :confused: im thinking root test. but how would i tell if its convergent or conditionally convergent?
2. ### Couple of converge/diverge sequences.. Don't understand

For this one I did 3^((5+3n)/n) and I got the sequence converges to the square root of 27 and put that in but I was wrong. This one I did 2^n/9^n and I got that the sequence converges to 2/9 but I was wrong again. I don't understand why I am wrong.. Isn't this the correct way to solve it?
3. ### Improper integral converge/diverge

Can anyone check my work here and if I went wrong, tell where and how and why etc etc. Thanks! Question: Decide whether the improper integral converges or diverges and if it converges, give it's value: \int_0^9 \frac {1} {\sqrt{9-x}} \, dx discontinuous at x=9, so rewrite the right...
4. ### Can someone please check my work here? (Improper integrals, converge/diverge)

I have the following two problems I am working on: For this one I am using the limit comparison test, I did f(x)= 1/(x^3-1)^1/2 / g(x) = 1/x which ended up at x/(x^3-1)^1/2 which I can determine as x->infty is going to be greater than 0 but less than infinity (thus both either converge...
5. ### Converge/Diverge help

I have to determine whether these series converge or diverge and i got stuck on 2 of them the first one is 1/ (n) (squareroot n) and the second one is n-1/(n^2) (squareroot n) any idelas how to do either of these two? Thanks
6. ### Calc 2: Converge/Diverge

How do i find out if these converge/diverge: inifinity SIGMA sqrt(2n+1)/(n^2) n=1 infinity SIGMA (3^K+K)/(K!) k=1 I dont know what K! is and i dont know what to do with the square root. It stumps me and I dont know what theorems to use. The integral test? Bounded sum...
7. ### converge/diverge

sum n=1 oo (arctan(n))^2 / 1+n^2 how do i solve it using integral test?