`(i)1/sqrt(2)+sqrt(3)+1/sqrt(2)`

The value of (1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+1/(sqrt(3)+sqrt(4))+........+(1)/(sqrt(8) + sqrt(9)) is

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

([(sqrt(2)+i sqrt(3))+(sqrt(2)-i sqrt(3))])/([(sqrt(3)+1sqrt(2))+(sqrt(3)-1sqrt(2))])

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

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

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

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

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

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