$ \sum_{n=1}^{\infty}\cfrac{\pi + \tan^{-1}n}{n\sqrt{n}+n+1}$
Hi all, these are questions from my graded math homework. For the first qn, I don't know how to proceed, coz of the inverse tan function. I'm clueless on whether i should use Comparison Test or Limit Comparison Test. Any ideas?
$ \sum_{n=1}^{\infty}\frac{\sqrt[4]{2n^8-4n^4+n}}{\sqrt[3]{n^7-3n^5+n^3}}$
For the second question, i am using Limit Comparison Test with $\cfrac{\sqrt[4]{2n^8}}{\sqrt[3]{n^7}}$ as the denominator, and the limit is 1. Since 1 is a positive real number, I can deduce that the series is divergent as $\cfrac{\sqrt[4]{2n^8}}{\sqrt[3]{n^7}}$ is divergent. Is this correct?