Question

\[\sum_{n=1}^{\infty} \frac{\sqrt(n^{2}-1)}{n^{3}+2n^{2}+5}\]
limit comparison test
\[\frac{\sqrt(n^{2})}{n^{3}}\]
\[\lim_{n \rightarrow\infty} \frac{1}{n} =0 \] convergent
correct?

Answer 1

Yes.

Answer 2

YESS!

Answer 3

BEST ANSWER!

Answer 4

thank you

Answer 5

\[ \sum_{n=1}^{\infty} \frac{\sqrt(n^{2}-1)}{n^{3}+2n^{2}+5} \leq \sum_{n=1}^{\infty} \frac{\sqrt{n^{2}}}{n^{3}} = \sum_{n=1}^{\infty} \dfrac{1}{n^2}\]
1/n^2 converges ... don't compare it with 1/n ... 1/n diverges.