Question

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Question the attachment !!

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Answer 1

Answer:

rationalizing all the denominators,

we get ,

$- 1 + \sqrt{2} - \sqrt{2} + \sqrt{3} - \sqrt{3} + \sqrt{4} ............ - \sqrt{8} + \sqrt{9}$

all are cancelled except :-

$- 1 + \sqrt{9}$

= -1 + 3

= 2 .

hence proved

Answer 2

Rationalize It

1/√2+1 = √2-1

Similarly= 1/√3+√2 = √3-√2

Similarly = 1/√4+√3 = √4-√3

Similarly = 1/√5+√4 = √5-√4

Similarly = 1/√6+√5 = √6-√5

Similarly = 1/√7+√6 = √7-√6

Similarly = 1/√8+√7 = √8-√7

Similarly = 1/√9+√8 = √9-√8

Add

√2-1+√3- √2+√4- √3+ √5-√4+√6-√5+√7-√6+√8-√7+√9-√8

-1+3 = 2