Question

plz answer the question​

Answer 1

Step-by-step explanation:

hope this helps you and look the answer once

Answer 2

Answer:

$\mathtt\purple{❖SOLUTION:-}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \:$

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

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

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

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

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

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

$= - 1 + \sqrt{9}$

$= - 1 + \sqrt{3 \times3}$

$= - 1 + 3$

$= 2$

$\mathtt\purple{HENCE \: , VERIFIED}$