Answer
Divergent
Work Step by Step
Let us consider $f(x)=\dfrac{1}{x+4}$
Here, the function $f(x)$ is positive, continuous and decreasing for $x \geq 1$
Then $\int_1^\infty \dfrac{1}{x+4} dx= \lim\limits_{k \to \infty} \int_1^k \dfrac{1}{x+4} dx=\lim\limits_{k\to \infty} [\ln |x+4|]_1^k$
and $\lim\limits_{k \to \infty} [\ln |k+4|-\ln 5]= \infty$
Thus, the sequence $\Sigma_{n=1}^\infty \dfrac{1}{n+4}$ is Divergent