Test series for convergence / divergence using a comparison test:
$$\sum_{n=1}^\infty\frac{n^2+1}{n^3+2}$$
Now, If it would be $$\sum_{n=1}^\infty\frac{n^2+1}{n^3-2}$$ then I could compare it as greater or equal to 1/n series which diverges, but since it is + 2 in the denominator then I am not sure what to do?
Best Answer
You don't need to compare starting at $1$. You have $$ \sum_{n=2}^\infty\frac{n^2+1}{n^3+2}\geq\sum_{n=2}^\infty \frac{n^2}{n^3+n^3}=\frac12\,\sum_{n=2}^\infty\frac1n=\infty. $$