Answer by Anne Bauval for Why $\lim\limits_{n \to \infty}...
This equality is purely algebraic. Forget about the...
View ArticleAnswer by the_candyman for Why $\lim\limits_{n \to \infty}...
Let $s = \sqrt{n+1}$ and $t = \sqrt{n}.$ Then:$$\mathcal{L} = \lim_{n \to \infty} \frac{\frac{1}{\sqrt{n+1}}}{\sqrt{n+1}-\sqrt{n}} = \lim_{n \to \infty} \frac{\frac{1}{s}}{s-t} = \\= \lim_{n \to...
View ArticleAnswer by Sebastiano for Why $\lim\limits_{n \to \infty}...
We have,$$\lim_{n \to \infty} \frac{\frac{1}{\sqrt{n+1}}}{\sqrt{n+1}-\sqrt{n}} = \lim_{n \to \infty}\left(\frac{1}{\sqrt{n+1}}\cdot \frac{1}{\sqrt{n+1}-\sqrt{n}}\cdot \frac{\sqrt{n+1} +...
View ArticleWhy $\lim\limits_{n \to \infty}...
I just need clarification about answer to this question:$$\lim_{n \to \infty} \frac{\sum\limits_{i = 1}^{n} \frac{1}{\sqrt{i}}}{\sqrt{n}} = \lim_{n \to \infty} \frac{\sum\limits_{i = 1}^{n+1}...
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