tex]...

July 2022 1 5 Report

СРОЧНО ДАЮ 35 БАЛЛОВ АЛГЕБРА
Упростить выражение
[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]

Answers & Comments

QDominus

Verified answer

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

Ответ: 13.

2 votes Thanks 2

Answers & Comments

Verified answer

tex]...

geometriya 9 klass zadali kanikulyarku pomogite reshit pozhalujsta

tex ac v kakom otnoshenii mn delit otrezok ab

kakoj gruz mozhno podnyat s pomoshyu podvizhnogo bloka prilozhiv silu k svobodnomu k

opredelite kolichestvo kornej uravneniya h2h aa2 v zavisimosti ot znacheniya

tex]...

opredelite kolichestvo kornej uravneniya 2h 3a h v zavisimosti ot znacheniya para

radiusy dvuh okruzhnostej ravny 8 i 3 sm a rasstoyanie mezhdu ih centrami 13 sm n

tex]...

algebra 8 klass s obyasneniem pozhalujsta76c0097ddd04c5a9502126c1a9f05779 27334

рекомендуемые вопросы

Helpful Links

Helpful Social