karoeiu/note_3^n.md Secret

Created September 6, 2021 06:12

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note_3^n.md

$\begin{align*} \lim _{n \to \infty} \frac{n^{3}}{3^{n}} &= \lim _{n \to \infty} \frac{n^{3}}{(1+2)^{n}} \\ &= \lim _{n \to \infty} \frac{n^{3}}{{}_nC_0+{}_nC_1 \cdot 2+{}_nC_2 \cdot2^{2} \cdots} \\ &< \lim _{n \to \infty} \frac{n^{3}}{{}_nC_0+{}_nC_1 \cdot 2 \cdots {}_nC_4 \cdot2^{4}} \\ &= 0 \end{align*}$

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