Answer
Divergent
Work Step by Step
Consider $f(x)=\dfrac{-2}{n+1}$
or, $f(x)=\dfrac{-2}{n+1}=-2(\dfrac{1}{n+1})$
Now, take the integral test to find the convergence and divergence for the sequence.
We have $\lim\limits_{x \to \infty} \int_0^\infty \dfrac{1}{ x+1}dx= \lim\limits_{a \to \infty} [\log (x+1)]_{0}^\infty=\infty$
Hence, the sequence $\Sigma_{n=0}^\infty \dfrac{-2}{ n+1}$ is Divergent.
