query: What is the limit of $ \sqrt[n]{ a^ n + b^ n}$ when $n \to \infty$ for $a,b ≥ 0$
positive_passages.docid: 144713
positive_passages.text: Simple Calculus Proof
negative_passages.docid: 83634
negative_passages.text: Find $\lim_{n\to \infty}\sqrt[n]{3^n+5^n}$
negative_passages.docid: 15982
negative_passages.text: Limit of $b_n$ when $b_n=\frac{a_n}{n}$ and $\lim\limits_{n\to\infty}(a_{n+1}-a_n)=l$
negative_passages.docid: 67084
negative_passages.text: Prove or disprove that $\lim_{n \to \infty} {n \choose k} / a^n = 0$ for all $k \in \mathbb{Z_+}, a \in \mathbb{R}: a> 1$.
negative_passages.docid: 5728
negative_passages.text: How to prove $\lim_{n \to \infty} \sqrt{n}(\sqrt[n]{n} - 1) = 0$?
negative_passages.docid: 128882
negative_passages.text: Prove $\lim\limits_{n\to\infty}\frac{1}{\sqrt[n]{n!}}=0$
negative_passages.docid: 4024
negative_passages.text: Finding the limit of $\frac {n}{\sqrt[n]{n!}}$
negative_passages.docid: 148320
negative_passages.text: Find the limit $\lim_\limits{n\to{\infty}}n^2(\sqrt[n]{x}-\sqrt[{n + 1}]{x})$ and my inquiry about Stolz-Cesàro theorem
negative_passages.docid: 26783
negative_passages.text: If $(1+\sqrt{2})^n=a_{n}+b_{n}\sqrt{2}\;,(\forall n\in \mathbb{N}).$Then $\lim_{n\rightarrow \infty}\frac{a_{n}}{b_{n}} = $
negative_passages.docid: 22347
negative_passages.text: Proving that: $\lim\limits_{n\to\infty} \left(\frac{a^{\frac{1}{n}}+b^{\frac{1}{n}}}{2}\right)^n =\sqrt{ab}$
negative_passages.docid: 147514
negative_passages.text: How to calculate $\lim \limits_{n \to \infty}(1 +\frac{a}{n})^n$?
negative_passages.docid: 151593
negative_passages.text: Prove that the limit of $\sqrt{n+1}-\sqrt{n}$ is zero
negative_passages.docid: 17289
negative_passages.text: prove $\sqrt{a_n b_n}$ and $\frac{1}{2}(a_n+b_n)$ have same limit
negative_passages.docid: 119145
negative_passages.text: $\lim\limits_{n\rightarrow\infty} \sqrt{n}(\sqrt{n+1}-\sqrt{n})$
negative_passages.docid: 48985
negative_passages.text: Calculating $\lim_{x\to+\infty}(\sqrt{x^2-3x}-x)$
negative_passages.docid: 133244
negative_passages.text: Finding $\lim_{n \to \infty} n(\sqrt[n]{2} - 1)$
negative_passages.docid: 128324
negative_passages.text: How do I take the limit as $n$ goes to $\infty$ of $\frac{\sqrt{n}}{\log(n)}$?