Show $\lim\limits_{n\to\infty} \dfrac{n^2+3^{2n}}{(n^3+3^n)^2} = 1$ Could you help me show that
$$\lim\limits_{n\to\infty} \dfrac{n^2+3^{2n}}{(n^3+3^n)^2} = 1$$

$$\lim\limits_{n\to\infty} \dfrac{n^2+3^{2n}}{(n^3+3^n)^2} =\lim_{n\to\infty}{n^2+3^{2n}\over n^6+2n^33^n+3^{2n}}=\lim_{n\to\infty}{\frac{n^2}{3^{2n}}+1\over\frac{n^6}{3^{2n}}+2\frac{n^3}{3^n}+1}=1$$
