I'm trying to convince myself that the following trigonometric series converges for all values of x
$\sum_{n=1}^\infty \dfrac{sin(nx)+cos(nx)}{n^2}$
my approach to the ratio test was following:
$\lim_{n \to \infty}\dfrac{\dfrac{sin(nx+x)+cos(nx+x)}{n^2(1+\dfrac{2}{n}+\dfrac{1}{n^2})}}{\dfrac{sin(nx)+cos(nx)}{n^2}}$
and I'm confused what to do next when I cancel $n^2$ terms and equate polynomials with $n$ in denominator to $0$.