Answer
Converges
Work Step by Step
Consider $a_n=\dfrac{7}{(2n+5)^n}$
By the Root Test $l=\lim\limits_{n \to \infty} \sqrt [n] {|a_n|}=\lim\limits_{n \to \infty} |a_n|^{1/n}$
$l=\lim\limits_{n \to \infty} |a_n|^{1/n}=\lim\limits_{n \to \infty}|\dfrac{\sqrt [n] 7}{{\sqrt [n] {(2n+5)^n}}}|=\lim\limits_{n \to \infty} \dfrac{1}{(2n+5)}$
or, $=\dfrac{1}{\infty}$
so, $l =0\lt 1$
Thus , the given series converges by the Root Test.
