<s>[INST] Finding $\lim_{n \to \infty} \frac{2^{n+1} + 3^{n+1}}{2^{n}+3^{n}}$ I need help with finding 
$\displaystyle \lim_{n \to \infty} \frac{2^{n+1} + 3^{n+1}}{2^{n}+3^{n}}$
Thanks!
 [/INST] $$
\lim_{n \to \infty} \frac{2^{n+1} + 3^{n+1}}{2^{n}+3^{n}} = \lim_{n \to \infty} \frac{(\frac{2}{3})^{n+1} + 1}{(\frac{1}{3})(\frac{2}{3})^{n}+\frac{1}{3}} = \frac{\,\,1\,\,}{\frac{1}{3}} = 3
$$
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