Answer
Converges
Work Step by Step
We have: $a_k=k^{11}$ and $b_k=k^{11}+3$
Now, we need to apply the limit comparison test.
$L=\lim\limits_{k \to \infty}\dfrac{a_k}{b_k}\\=\lim\limits_{k \to \infty}\dfrac{k^{11}}{k^{11}+3}\\=\lim\limits_{k \to \infty} \dfrac{1}{1+\dfrac{3}{k^{11}}} \\=1$
Therefore, the series converges by the limit comparison test.
