[tex]\lim_{n \to \infty} \frac{2x^{n+1}-3x^{n+2}}{3x^{n+2}}= \lim_{n \to \infty} \left(\frac{2x^{n+1}}{3x^{n+2}}- \frac{3x^{n+2}}{3x^{n+2}}\right)=\lim_{n \to \infty} \left(\frac{2x^{n+1}}{3x*x^{n+1}}- 1}\right)=\lim_{n \to \infty} \left(\frac{2}{3x}- 1}\right)=-1[/tex]