Question

(1/1+√2)+(1/√2+√3)+(1/√3+√4)+(1/√4+√5)+(1/√5+√6)+(1/√6+√7)+(1/√7+√8)+(1/√8+√9)

How to solve????

Answer 1

1/1+root2=( 1/1+root2)(root2-1/root2-1)
since by rationalisation
=root2-1/1
similarly for all
we get
-1+root9
=3-1
=2

Answer 2

I hope it's helps you