=(√2- 1)/( 1+√2)(√2- 1)
=√2- 1
Similarly, 1/(√ 3+√ 2) = √ 3-√ 2. ...
Original formula = √ 2-1+√ 3-√ 2+...+√100-√ 99.
=√ 100- 1
= 10- 1
=9