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

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

What is the value of (1/(sqrt(9) - sqrt(8)) - 1/(sqrt(8) - sqrt(7)) + 1/(sqrt(7) - sqrt(6)) - 1/(sqrt(6) - sqrt(5)) + 1/(sqrt(5) - sqrt(4))) ?

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

The sum of 1/(sqrt(2)+1) + 1/(sqrt(3) + sqrt(2)) + 1/(sqrt(4) + sqrt(3)) +.....1/(sqrt(100) + sqrt(99)) is equal to:

(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))