Question

No 13 plz quick plz. Will mark you the brainliest

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

$\frac{1 }{1 + \sqrt{2} } + \frac{1}{ \sqrt{2} + \sqrt{3} } + \frac{1}{ \sqrt{3} + \sqrt{4} } + .......... + \frac{1}{ \sqrt{8} + 3} \\ \\ = \frac{1 }{1 + \sqrt{2} } + \frac{1}{ \sqrt{2} + \sqrt{3} } + \frac{1}{ \sqrt{3} + \sqrt{4} } + .......... + \frac{1}{ \sqrt{8} + \sqrt{9} } \\ \\ = (\frac{1 }{1 + \sqrt{2} } )( \frac{ \sqrt{2} - 1}{ \sqrt{2} - 1 } )+ ( \frac{1}{ \sqrt{2} + \sqrt{3} })( \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} - \sqrt{2} }) + (\frac{1}{ \sqrt{3} + \sqrt{4} } )( \frac{ \sqrt{4} - \sqrt{3} }{ \sqrt{4} - \sqrt{3} }) + .......... + \frac{1}{ \sqrt{8} + \sqrt{9} } ( \frac{ \sqrt{9} - \sqrt{8} }{ \sqrt{9} - \sqrt{8} } ) \\ \\ = \sqrt{2} - 1 + \sqrt{3} - \sqrt{2} + \sqrt{4} - \sqrt{3} + \sqrt{5} - \sqrt{4} + \sqrt{6} - \sqrt{5} + \sqrt{7} - \sqrt{6} + \sqrt{8} - \sqrt{7} + \sqrt{9} - \sqrt{8} \\ \\ = \sqrt{9} - 1 \\ \\ = 3 - 1 \\ \\ = 2$

hope it helps