Answer
Divergent
Work Step by Step
We have: $\Sigma_{n=1}^\infty \dfrac{n}{n+10}$
and $\lim\limits_{n \to \infty} \dfrac{n}{n+10}=\lim\limits_{n \to \infty} \dfrac{n}{n(1+\dfrac{10}{n})}$
Now, $\lim\limits_{n \to \infty} \dfrac{n}{n(1+\dfrac{10}{n})}=\dfrac{\lim\limits_{n \to \infty} 1}{\lim\limits_{n \to \infty}
1+ \lim\limits_{n \to \infty} \dfrac{10}{n}}=\dfrac{1}{1+0}=1$
This shows a divergent series in accordance to the nth-Term Integral Test.
