$ \lim\limits_{n\to\infty}\frac{2^n}{3^{\frac{n}{2}}}$
I used wolfram to get the limit as follows: "lim n tends infinity 2^n/3^(n/2)".
And using L'Hospital's rule the result was: $\displaystyle\frac{2^{n+6}}{3^{\frac{n}{2}}}$, which tends to infinity.
My question is why does $\displaystyle\frac{2^{n+6}}{3^{\frac{n}{2}}}$ tend to infinity?