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)]

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Question 1140877: Without a calculator find, 1/[sqrt(1) + sqrt(2)] + 1/[sqrt(2) + sqrt(3)] + 1/[sqrt(3) + sqrt(4)] + ...+ 1/[sqrt(15) + sqrt(16)]
Answer by ikleyn(52780)   (Show Source): You can put this solution on YOUR website!
.
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.

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See the lesson
    - Amazing calculations with fractions that contain quadratic irrationalities in denominators, Problem 4
in this site.


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