Question

Determine if convergent or divergent using comparison tests

Answer 1

`\displaystyle\sum_(k\ge1)\frac{\sqrt[3]{k^2+1}}{√(k^3+2)}\sim\sum_(k\ge1)(k^(2/3))/(k^(3/2))=\sum_(k\ge1)\frac1{k^(5/6)}`

Recall that
`\displaystyle\sum_(k\ge1)\frac1{k^p}` diverges for
`0\le p\le1`. 5/6 falls in this interval, so this series must diverge, and so must the original one by comparison.