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[" 3.Show that "],[qquad (1)/(sqrt(2)+1)...

[" 3.Show that "],[qquad (1)/(sqrt(2)+1)+(1)/(sqrt(3)+sqrt(2))+(1)/(sqrt(4)+sqrt(3))+...+(1)/(sqrt(9)+sqrt(8))=2]

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(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))

(1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))+...(1)/(sqrt(99)+sqrt(100))

Prove that : (1)/(sqrt(2)+1)+ (1)/(sqrt(3)+sqrt(2))+ (1)/(2+sqrt(3))=1

Prove that (1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))+....+(1)/(sqrt(8)+sqrt(9))=2

the value of 3(1)/(sqrt(2)+1)+(1)/(sqrt(3)+sqrt(2))+(1)/(sqrt(4)+sqrt(3))+.........+(1)/(sqrt(16)+sqrt(15)) is

1/(1-sqrt(2))+ 1/(sqrt(2)-sqrt(3))+1/(sqrt(3)-sqrt(4))+..........+1/(sqrt(8)-sqrt(9))

Simplify: (1)/(sqrt2 +1) + (1)/(sqrt3 + sqrt2) + (1)/(sqrt4 + sqrt3)

1/(sqrt3 + sqrt2) + 1/(sqrt3 -sqrt2)=