Answer
Converges
Work Step by Step
Let us consider $a_n=\dfrac{7}{(2n+5)^n}$
In order to solve the given series we will take the help of Root Test. This test states that when the limit $L \lt 1$, the series converges and for $L \gt 1$, the series diverges.In order to solve the series we will take the help of Root Test.
It can be defined as follows: $L=\lim\limits_{n \to \infty} \sqrt [n] {|a_n|}=\lim\limits_{n \to \infty} |a_n|^{1/n}$
Now, $L=\lim\limits_{n \to \infty} |a_n|^{1/n}=\lim\limits_{n \to \infty}|\dfrac{\sqrt [n] 7}{{\sqrt [n] {(2n+5)^n}}}|$
so, $L=\lim\limits_{n \to \infty} \dfrac{1}{(2n+5)}=\dfrac{1}{\infty}=0\lt 1$
Hence, the series converges by the Root Test.