0
votes
1answer
23 views

Radius of Convergence Problem solving

I did this questions using the Ratio Test which showed that the radius of convergence is the same. I'm not sure if that is correct. (I am having my doubts about c_n becoming c_n+1 for the ratio test ...
3
votes
0answers
162 views

Cluster point of $a_{n}:=n+(-1)^{n}n$

I am trying to find the cluster point of the sequence $a_{n}:=n+(-1)^nn$. Can you please check my solution? The subsequence diverges for increasing even $n$ since $2n$ grows infinitely. The ...
1
vote
3answers
57 views

need help - $\lim_{n \to \infty} i^{3n} $

it seems first easy to me, but now i am tossing my head against wall not being able to solve the problem. i need to check for convergence of this sequence below. i dont know how to start although it ...
2
votes
2answers
47 views

simple convergence test $\lim_{n \to \infty} \frac{2^{n+1}+3^{n+1}}{2^n+3^n}$

i am pulling my hair out in solving this problem. i know, it is a stupid question but i am not that good at maths, and many thanks for any help $\lim_{n \to \infty} \frac{2^{n+1}+3^{n+1}}{2^n+3^n}$ ...
1
vote
2answers
54 views

solve $\lim_{n \to \infty} \frac{(-2)^n}{3^{2n}} $

i am eating myself not being able to solve this problem. i somehow feel that the sequence converges to $0$, but once i calculate, it is not coming to that result. or am i making stupid mistake on the ...
0
votes
1answer
53 views

solve $\lim_{n \to \infty}\left( \frac{3+2n}{\sqrt{3}+\sqrt{2}n} + i\,n\right)$

I am checking this sequence for convergence but i am not sure whether i am on the right path in calculations, these steps are what i am doing now. $\infty + n$ will go to infinity, right? $$\lim_{n ...