SOLUTION: Compute the sum {1}/{sqrt{100} + sqrt{102}} + {1}/{sqrt{102} + sqrt{104}} + {1}/{sqrt{104}+sqrt{106}} + ...+ {1}/{sqrt{9998} + sqrt{10000}}.

Question 1066672: Compute the sum
{1}/{sqrt{100} + sqrt{102}} + {1}/{sqrt{102} + sqrt{104}} + {1}/{sqrt{104}+sqrt{106}} + ...+ {1}/{sqrt{9998} + sqrt{10000}}.

Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.

 = multiply the numerator and denominator by  (rationalizing the denominator) to get = .


Do it with every atom in your long molecule.

Then add.


Everything inside will cancel.


Only two terms survive: very first and very last.


So, the sum is


 -  =  = -5 - (-50) = 45.

SOLVED.

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