convergence

[cazza90]

so I'm asked to talk about the convergence of (2n+7)/cube root((n^8) + (N^3))

I did the limit comparison test and used bn as 2/n^(5/3), and got 1 as my answer - my notes say that a limit greater than 0 just means they either converge or diverge together? so essentially i got nowhere? what should I do now?

 

[DrSteve]

\(\displaystyle \Sigma \frac{1}{n^{5/3}}\) is a p-series with p>1, thus it converges.