I am having a hard time with this problem: I tried by using the sandwich theorem but I failed.
$\lim\limits_{n\to\infty} \dfrac{n^b}{a^n}= 0\;,\;$ when $\;a > 1,\; b > 0\;.$
Could anyone please help me?
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A stronger result is true: $\sum \frac {n^{b}} {a^{n}}$ is convergent: Apply ratio test. – Kavi Rama Murthy Apr 30 '21 at 12:03
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Could you please show me how to do it. I have no idea. – Miguel Bets Apr 30 '21 at 12:04
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This is a well-known fact: Exponential function grows faster, than any polynomial. – lone student Apr 30 '21 at 12:04