Answer
Converges
Work Step by Step
Here, we are given that $a_1=2; a_{n+1}=\dfrac{2n+1}{5n-4} a_n$
Thus, $\dfrac{a_{n+1}}{a_n}=\dfrac{2n+1}{5n-4}$
Next, we have: $\lim\limits_{n \to \infty}|\dfrac{a_{n+1}}{a_n}|=\lim\limits_{n \to \infty} \dfrac{2n+1}{5n-4}=\dfrac{2}{5} \lt 1$
Hence, we can conclude that the given series converges.
