Answer
Convergent
Work Step by Step
Given: $f(x)=\Sigma_{n=1}^{\infty}\frac{1}{(2n+1)^{3}}$
$\int_1^\infty f(x)dx=\int_1^\infty \frac{1}{(2x+1)^{3}}dx$
$=-\frac{1}{4}[(2x+1)^{-2}]_{1}^{\infty}$
$=\frac{1}{36}$
Hence, the given series converges.