Question

If $\frac{1}{\sqrt{0.\overline{2}}+\sqrt{0.\overline{4}}}+\frac{1}{\sqrt{0.\overline{4}}+\sqrt{0.\overline{6}}}+\frac{1}{\sqrt{0.\overline{6}}+\sqrt{0.\overline{8}}}+\frac{1}{\sqrt{0.\overline{10}}+\sqrt{0.\overline{12}}}+\frac{1}{\sqrt{0.\overline{12}}+\sqrt{0.\overline{14}}}+\frac{1}{\sqrt{0.\overline{14}}+\sqrt{0.\overline{16}}}+\frac{1}{\sqrt{0.\overline{16}}+\sqrt{0.\overline{18}}}+......$

$...............+\frac{1}{\sqrt{0.\overline{38}}+\sqrt{0.\overline{40}}}=\frac{3}{2}\left(\sqrt{a}+\sqrt{b}\right),$ where a > b, a and b are rational numbers, then (a ÷ b) is

यदि $\frac{1}{\sqrt{0.\overline{2}}+\sqrt{0.\overline{4}}}+\frac{1}{\sqrt{0.\overline{4}}+\sqrt{0.\overline{6}}}+\frac{1}{\sqrt{0.\overline{6}}+\sqrt{0.\overline{8}}}+\frac{1}{\sqrt{0.\overline{10}}+\sqrt{0.\overline{12}}}+\frac{1}{\sqrt{0.\overline{12}}+\sqrt{0.\overline{14}}}+\frac{1}{\sqrt{0.\overline{14}}+\sqrt{0.\overline{16}}}+\frac{1}{\sqrt{0.\overline{16}}+\sqrt{0.\overline{18}}}+......$

$...............+\frac{1}{\sqrt{0.\overline{38}}+\sqrt{0.\overline{40}}}=\frac{3}{2}\left(\sqrt{a}+\sqrt{b}\right),$ जहाँ a > b, a तथा b परिमेय संख्याएँ हैं, तब (a ÷ b ) का मान है

• A. 11
• B. 22
• C. 55
• D. 110

Answer 1

The correct option is C 55

Solution