[" 15.Wब क्रै) : "],[qquad (1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))]

x=(1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+2)=

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

Simplify: (1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(5))

(1+sqrt(2))/(sqrt(5)+sqrt(3))+(1-sqrt(2))/(sqrt(5)-sqrt(3))

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

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

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

1/(sqrt(2)+sqrt(3)+sqrt(5))+1/(sqrt(2)+sqrt(3)-sqrt(5))

Prove that (i) (1)/(3+sqrt(7)) + (1)/(sqrt(7)+sqrt(5))+(1)/(sqrt(5)+sqrt(3)) +(1)/(sqrt(3)+1)=1 (ii) (1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))+(1)/(sqrt(4)+sqrt(5))+(1)/(sqrt(5)+sqrt(6))+(1)/(sqrt(6)+sqrt(7)) +(1)/(sqrt(7)+sqrt(8))+(1)/(sqrt(8) + sqrt(9)) = 2

The sum of the series (1)/(sqrt(1)+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))+ . . . . .+(1)/(sqrt(n^(2)-1)+sqrt(n^(2))) equals