SOLUTION: Find the sum: {{{ 1/(sqrt(1)+sqrt(2)+sqrt(4))+1/(sqrt(4)+sqrt(6)+sqrt(9))+1/(sqrt(9)+sqrt(12)+sqrt(16))}}} P.S. to all tutors who are willing to solve this question, all

Question 1132142: Find the sum:

P.S. to all tutors who are willing to solve this question, all the square root signs are supposed to be cube roots. I just did not know how to insert the equation. ALL THE SQUARE ROOT SIGNS ARE SUPPOSED TO BE CUBE ROOTS!!!!!!
Answer by ikleyn(52780) (Show Source): You can put this solution on YOUR website!
.

So, the question is:

    Find the sum   +  +

Solution

Use the identity   = ,   which gives you

                   = .   <<<---=== it is how to "rationalize the fraction" in this case (!)


In this way,


 =  =               <<<---=== in this case a= 2;  b= 1.


 =  = ;            <<<---=== in this case a= 3;  b= 2.


 =  =            <<<---=== in this case a= 4;  b= 3.


So, the long sum of three fractions is equal to


 +  +  = .      ANSWER

Solved.

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