Solution:
\( \displaylines{\text{This behaves like }\sum_{}^{}\frac{1}{k}\text{, so we try a limit comparison test with the harmonic series.}\\ \lim_{k\to\infty}\frac{\frac{1}{k}}{\left(\frac{k^9}{k^{10}+3}\right)}=\lim_{k\to\infty}\frac{k^{10}+3}{k^{10}}=1\\ \text{This indicates the given series is also divergent.}} \)