Question

If a1, a2.....an are in an AP where a>0for all I there show that
1/(√a1+√a2)+1/(√a2+√a3)......+1/(√(an-1)+√an)=n-1/(√a1+√an)

Answer 1

Well this can be solved by two methods:

The first is quite a long and very usual method.
The second by a trick that i will tell you.

FROM THE QUESTION WE KNOW THAT a1 a2 a3 are in AP.

So let us assume a1=1,a2=2,a3=3.

Now put these values in the given question and if the expression is true and we will get same answer both sides.

Hope it helps.