Prove that: `1/(2+sqrt5)+1/(sqrt5+sqrt6)+1/(sqrt6+sqrt7)+1/(sqrt7+sqrt8)=2(sqrt2-1)`

1/(sqrt7 - sqrt6)

1/(sqrt7 - sqrt6)

1/(sqrt7 - sqrt6)

(sqrt7-sqrt6)/(sqrt7+sqrt6)-(sqrt7+sqrt6)/(sqrt7-sqrt6)=

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

1/(sqrt7+sqrt6-sqrt13)=

Simplify 1/sqrt2+1/(sqrt2+sqrt4)+1/(sqrt4+sqrt6)+1/(sqrt6+sqrt8)

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