SOLUTION: Without a calculator find, 1/[sqrt(1) + sqrt(2)] + 1/[sqrt(2) + sqrt(3)] + 1/[sqrt(3) + sqrt(4)] + ...+ 1/[sqrt(15) + sqrt(16)]

Every aggregate   is equal to  .


    // after multiplication the denominator and the numerator by  



After summing all such aggregates from m = 1 to m = 15 you get the final answer


    ,   which is equal to  4 - 1 = 3.


(all other intermediate terms cancel each other on the way).


ANSWER.  3.