Answer
Diverges
Work Step by Step
Here, we have the given series $\Sigma_{n=1}^{\infty} \dfrac{5 n}{2n-1}$
Next, we will use the nth divergence test for the given series to check whether it is convergent or divergent.
$\lim\limits_{n \to \infty} \dfrac{5n }{2n-1}=\lim\limits_{n \to \infty} \dfrac{5}{2-1/n}=\dfrac{5}{2+0}=\dfrac{5}{2} \ne 0$
Hence, we can conclude that the given series diverges by the nth divergence test .
