query: Find $\lim_{n \rightarrow +\infty} n^2(\sqrt[n]{a} - \sqrt[n+1]{a})$ for $a > 0$
positive_passages.docid: 148320
positive_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: 83634
negative_passages.text: Find $\lim_{n\to \infty}\sqrt[n]{3^n+5^n}$
negative_passages.docid: 31174
negative_passages.text: Find the limit if it exists of $S_{n+1} = \frac{1}{2}(S_n +\frac{A}{S_n})$
negative_passages.docid: 68609
negative_passages.text: Let $a_{n+1}=\sqrt{a_1+a_2+\cdots+a_n}$ .Prove that $ \lim\limits_{n \rightarrow \infty} \frac{a_n}{n}=\frac{1}{2}$
negative_passages.docid: 3527
negative_passages.text: Finding $\lim_{n \to \infty} \prod_{r=1}^n (1+ \frac{1}{a_r})$
negative_passages.docid: 42241
negative_passages.text: Evaluation of $\lim_{n\rightarrow \infty}\sum^{n}_{r=1}\frac{r}{n^2+n+r}$
negative_passages.docid: 46542
negative_passages.text: How do I calculate $\lim_{x\to+\infty}\sqrt{x+a}-\sqrt{x}$?
negative_passages.docid: 24695
negative_passages.text: How to solve the limit $\lim\limits_{n\to \infty}(1-a)(1-a^2)\cdots(1-a^n)$?
negative_passages.docid: 142708
negative_passages.text: Finding the limit $\lim_{n\rightarrow\infty}(1-\frac{1}{3})^2(1-\frac{1}{6})^2(1-\frac{1}{10})^2...(1-\frac{1}{n(n+1)/2})^2$
negative_passages.docid: 63023
negative_passages.text: Evaluation of $\lim_{x\rightarrow \infty}\sqrt{x^2+x+1} -\lfloor \sqrt{x^2+x+1 }\rfloor\;,$
negative_passages.docid: 112481
negative_passages.text: Given $a_{n+1} = \frac{{a_n}}{\sin({a_n})}$ with $0 < a_1 < \frac{\pi}{2}$. Show that the limit $\lim_{n\rightarrow\infty}{a_n}$ exists and find it.
negative_passages.docid: 12378
negative_passages.text: Find the limit $\displaystyle\lim_{n\rightarrow\infty}{(1+1/n)^{n^2}e^{-n}}$?
negative_passages.docid: 30834
negative_passages.text: limit of $\lim\limits_{x \to \infty}((x+1)^a - x^a)$
negative_passages.docid: 111418
negative_passages.text: Finding lim${_{n \rightarrow \infty}}\left( \frac{n^3}{2^n} \right)$
negative_passages.docid: 37260
negative_passages.text: Calculate $\lim_{n\to{+}\infty}{(\sqrt{n^{2}+n}-n)}$
negative_passages.docid: 16739
negative_passages.text: The Limit of $x\left(\sqrt[x]{a}-1\right)$ as $x\to\infty$.
negative_passages.docid: 140622
negative_passages.text: Find the value of : $\lim_{x \to \infty} \sqrt{4x^2 + 4} - (2x + 2)$