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Compute the sum \(\frac{1}{\sqrt{100} + \sqrt{102}} + \frac{1}{\sqrt{102} + \sqrt{104}} + \frac{1}{\sqrt{104}+\sqrt{106}}\)

 Jul 13, 2022
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Multiplying  top/bottom of each fraction by its conjugate  we get

 

[ sqrt 100 - sqrt 102] / -2   + [ sqrt 102 - sqrt 104 ] / -2  + [ sqrt 104 - sqrt 106] / -2   =

 

[ sqrt 100  -  sqrt 106 ]  / -2  =

 

[ sqrt 106  - sqrt 100]  / 2   =

 

(1/2) (sqrt [ 106] - 10 )

 

 

cool cool cool

 Jul 13, 2022

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