\displaystyle 1 \leq \frac{1 + \frac{6^n}{(10 + 3 \cos n)^n}}{1 + \frac{3^n}{(10 + 3 \cos n)^n}} \leq 1 + \frac{6^n}{(10 + 3 \cos n)^n} \leq 1 + \frac{6^n}{7^n}