I have tried using the ratio lemma to tackle this question and also the fact $(n+1)^k \geq 1 + nk$ and I haven't reached an answer. How should I go about solving this problem?
2026-04-03 06:17:42.1775197062
Find the limit of the sequence $ \frac{x^n}{n^k}$ as $n \to \infty$ for all values of$ x > $0 and $k = 1, 2,\cdots$
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HINT
$x\left (\frac{ n^{k}}{n+1^{k}} \right )= x\left ( \frac{n}{n+1} \right )^{k}=x\left ( \frac{n+1}{n} \right )^{-k}= x\left ( 1+\frac{1}{n} \right )^{-k}$