I think what I need to do is find the value of $n$ where $n^k. I know that this value occurs whenever $n>k\log_an$, however I don't understand how to interpret this result into a general $N$ to pick as a maximum for the sequence convergence. What am I missing here?
Let $k\in\mathbb{N}$ and $a>1$. Show that $\lim_{n\to\infty} \frac{n^k}{a^n}=0$.
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real-analysis