Prove that `1/(1+sqrt2) + 1/(sqrt2 +sqrt3) + 1/(sqrt3+sqrt4) + 1/(sqrt4+sqrt5) + 1/(sqrt5+sqrt6) + 1/(sqrt6+sqrt7) + 1/(sqrt7+ sqrt8) + 1/(sqrt8 + sqrt9) = 2 `

Prove that: 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

Prove that: 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

Prove that: 1/(3-sqrt8)-1/(sqrt8-sqrt7)+1/(sqrt7-sqrt6)-1/(sqrt6-sqrt5)+1/(sqrt5-2)=5

Simplify: 1/(sqrt5 + sqrt4) + 1/(sqrt4 + sqrt3) + 1/(sqrt3 + sqrt2) + 1/(sqrt2 + sqrt1)

The value of { 1/(sqrt6 - sqrt5) - 1/(sqrt5 - sqrt4) + 1/(sqrt4 - sqrt3) - 1/(sqrt3 - sqrt2) + 1/(sqrt2 - 1)} is :

Show that 1/(3+sqrt 7)+ 1/(sqrt7+sqrt5)+ 1/(sqrt5+sqrt3)+1/(sqrt3+1)=1

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

(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))