The value of (1 - √2) + (√2 - √3) + (√3 - √4) + . . . . . . + ($$\sqrt {15} $$ - $$\sqrt {16} $$ ) is-

Solution (By Examveda Team)

$$\eqalign{ & {\text{Expression}} \cr & = \left( {1 - \sqrt 2 } \right) + \left( {\sqrt 2 - \sqrt 3 } \right) + \left( {\sqrt 3 - \sqrt 4 } \right) + \,.\,.\,.\,.\, + \left( {\sqrt {15} - \sqrt {16} } \right) \cr & = 1 - \sqrt 2 + \sqrt 2 - \sqrt 3 + \sqrt 3 - \sqrt 4 + \,.\,.\,.\,.\, + \sqrt {15} - \sqrt {16} \cr & = 1 - \sqrt {16} \cr & = 1 - 4 \cr & = - 3 \cr} $$