Question

Предел limn→∞(2n−1−−−−−√−2n−−√) равен

Answer 1

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