Question

ПОЖАЛУЙСТА ВЫЧИСЛИТЕ СРОЧНО

Answer 1

Ответ:

9

Объяснение:

$\displaystyle\\\frac{1}{\sqrt{2}+1 }\cdot\frac{\sqrt{2}-1}{\sqrt{2}-1} =\frac{\sqrt{2}-1}{2-1} = \sqrt{2}-1\\\\\\\frac{1}{\sqrt{3}+\sqrt{2} }\cdot\frac{\sqrt{3}-\sqrt{2} }{\sqrt{3}-\sqrt{2} } =\frac{\sqrt{3}-\sqrt{2} }{3-2} = \sqrt{3}-\sqrt{2} \\\\...\\\\\frac{1}{\sqrt{100}+\sqrt{99} }\cdot\frac{\sqrt{100}-\sqrt{99} }{\sqrt{100}-\sqrt{99} } =\frac{\sqrt{100}-\sqrt{99} }{100-99} = \sqrt{100}-\sqrt{99}$

тогда

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