=(√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