Question

give me the answer ​

Answer 1

Answer:

Option c is correct answer..........

Answer 2

Step-by-step explanation:

$= \frac{1}{ \sqrt{2} + 1 } + \frac{1}{ \sqrt{3} + \sqrt{2} } + \frac{1}{ \sqrt{4} + \sqrt{3} } + \frac{1}{ \sqrt{5} + \sqrt{4} } + \frac{1}{ \sqrt{6} + \sqrt{5 } } + \frac{1}{ \sqrt{7} + \sqrt{6} } + \frac{1}{ \sqrt{8} + \sqrt{7} } + \frac{1}{ \sqrt{9} + \sqrt{8} } \\ rationalise \: the \: denominator \\ = (\frac{1}{ \sqrt{2} + 1 } \times \frac{\sqrt{2} - 1}{\sqrt{2} - 1} ) + (\frac{1}{ \sqrt{3} + \sqrt{2} } \times \frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} - \sqrt{2}} ) + ( \frac{1}{ \sqrt{4} + \sqrt{3} } \times \frac{\sqrt{4} - \sqrt{3}}{\sqrt{4} - \sqrt{3}}) + ( \frac{1}{ \sqrt{5} + \sqrt{4} } \times \frac{\sqrt{5} - \sqrt{4}}{\sqrt{5} - \sqrt{4}}) + (\frac{1}{ \sqrt{6} + \sqrt{5 } } \times \frac{\sqrt{6} - \sqrt{5 } }{\sqrt{6} - \sqrt{5 } } )+ (\frac{1}{ \sqrt{7} + \sqrt{6} } \times \frac{\sqrt{7} - \sqrt{6}}{\sqrt{7} - \sqrt{6}} ) + (\frac{1}{ \sqrt{8} + \sqrt{7} } \times \frac{ \sqrt{8} - \sqrt{7} }{ \sqrt{8} - \sqrt{7} } )+( \frac{1}{ \sqrt{9} + \sqrt{8} } \times \frac{ \sqrt{9} - \sqrt{8} }{\sqrt{9} - \sqrt{8} } ) \\ = \frac{\sqrt{2} - 1}{2 - 1} + \frac{ \sqrt{3} - \sqrt{2} }{3 - 2} + \frac{ \sqrt{4} - \sqrt{3} }{4 - 3} + \frac{ \sqrt{5} - \sqrt{4} }{5 - 4} + \frac{ \sqrt{6} - \sqrt{5} }{6 - 5} + \frac{ \sqrt{7} - \sqrt{6} }{7 - 6} + \frac{ \sqrt{8} - \sqrt{7} }{8 - 7} + \frac{ \sqrt{9} - \sqrt{8} }{9 - 8} \\ = (\sqrt{2} - 1) + ( \sqrt{3} - \sqrt{2} ) + ( \sqrt{4} - \sqrt{3} ) + ( \sqrt{5} - \sqrt{4} ) + ( \sqrt{6} - \sqrt{5} ) + ( \sqrt{7} - \sqrt{6} ) + ( \sqrt{8} - \sqrt{7} ) + ( \sqrt{9} - \sqrt{8} ) \\ = - 1 + \sqrt{9}$