<s>[INST] Show $\lim\limits_{n\to\infty} \dfrac{n^2+3^{2n}}{(n^3+3^n)^2} = 1$ Could you help me show that
$$\lim\limits_{n\to\infty} \dfrac{n^2+3^{2n}}{(n^3+3^n)^2} = 1$$
 [/INST] $$\dfrac{n^2+3^{2n}}{(n^3+3^n)^2}  = \frac{1 + \frac{n^2}{3^{2n}}}{\left( 1 + \frac{n^3}{3^{2n}}\right)^2}$$
As exponential grows more faster than polynomial, you have $1/1$
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