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СРОЧНО ДАЮ 35 БАЛЛОВ АЛГЕБРА
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[tex]\frac{1}{\sqrt{2}+1 }+\frac{1}{\sqrt{3}+\sqrt{2}}+\frac{1}{\sqrt{4}+\sqrt{3}}+\frac{1}{\sqrt{5}+\sqrt{4}}+...+\frac{1}{\sqrt{196}+\sqrt{195}}[/tex]

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QDominus

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$\frac{1}{1 + \sqrt{2} } + \frac{1}{ \sqrt{2} + \sqrt{3} } + \frac{1}{ \sqrt{3} + \sqrt{4} } + ... + \frac{1}{ \sqrt{195} + \sqrt{196} } = \\ = \frac{1 - \sqrt{2} }{(1 + \sqrt{2})(1 - \sqrt{2} )} + \frac{ \sqrt{2} - \sqrt{3} }{ (\sqrt{2} + \sqrt{3}) ( \sqrt{2} - \sqrt{3}) } + ... + \frac{ \sqrt{195} - \sqrt{196} }{ (\sqrt{195} + \sqrt{196})( \sqrt{195} - \sqrt{196} ) } = \\ = - 1 + \sqrt{2} + \sqrt{3} - \sqrt{2} + \sqrt{4} - \sqrt{3} + ... + \sqrt{196} - \sqrt{195} = - 1 + \sqrt{196} = 14 - 1 = 13$

Ответ: 13.

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