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