Question

Предел limn→∞(2n−1−−−−−√−2n−−√) равен

Answer 1

$\displaystyle\lim_{n \to \infty} (\sqrt{2n-1}-\sqrt{2n})= \lim_{n \to \infty}\frac{(\sqrt{2n-1}-\sqrt{2n})(\sqrt{2n-1}+\sqrt{2n})}{\sqrt{2n-1}+\sqrt{2n}}=\\ \\ \\ = \lim_{n \to \infty} \frac{2n-1-2n}{\sqrt{2n-1}+\sqrt{2n}}=\lim_{n \to \infty} \frac{-1}{\sqrt{2n-1}+\sqrt{2n}}=\lim_{n \to \infty} \frac{-\frac{1}{n}}{\sqrt{2-\frac{1}{n}}+\sqrt{2}}=0$