Question

ПОМОГИТЕ СРОЧНО АЛГЕБРА ДАЮ 30 БАЛЛОВ​

Answer 1

$\frac{1}{\sqrt{n+1}+\sqrt n}=\frac{\sqrt{n+1}-\sqrt n}{(\sqrt{n+1}+\sqrt n)(\sqrt{n+1}-\sqrt n)}=\\\\\frac{\sqrt{n+1}-\sqrt n}{n+1-n}=\sqrt{n+1}-\sqrt n$

$\frac{1}{\sqrt{2}+1}+\frac{1}{\sqrt{3}+ \sqrt{2} }+\frac{1}{\sqrt{4}+ \sqrt{3} }+...+\frac{1}{\sqrt{100}+ \sqrt{99} }=$

$\sqrt{2}-1+ \sqrt{3} - \sqrt{2} + \sqrt{4}- \sqrt{3}+...+ \sqrt{100}- \sqrt{99} =-1+ \sqrt{100}=-1+10=9$

Ответ: 9