Mathematics, 18.10.2021 17:20, nicktroutt27

$\frac{1}{1 + \sqrt{2} } + \frac{1}{ \sqrt{2 + \sqrt{3} } } + \frac{1}{ \sqrt{3 + \sqrt{4} } } + \frac{1}{ \sqrt{5 + \sqrt{6} } } + \frac{1}{ \sqrt{6 + \sqrt{7} } } + \frac{1}{ \sqrt{7 + \sqrt{8} } } + \frac{1}{ \sqrt{8 + \sqrt{9} } } = 2$ mister brainless i want full explanation

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mister brainless i want full explanation...