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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}} + \cdots + \frac{1}{\...

Guest Jan 31, 2015

Best Answer 

 #1
avatar+92699 
+10

1/ (√102 + √100) = (√102 - √100)/ 2

And

1/ (√104 + √102) = (√104 - √102)/ 2

So, all fractions would have the same denominators, and all the "intermediate" terms would "cancel" leaving us with

[√10000 - √100]/ 2 =

[100-10] /2 =

90/2 =

45

CPhill  Jan 31, 2015
 #1
avatar+92699 
+10
Best Answer

1/ (√102 + √100) = (√102 - √100)/ 2

And

1/ (√104 + √102) = (√104 - √102)/ 2

So, all fractions would have the same denominators, and all the "intermediate" terms would "cancel" leaving us with

[√10000 - √100]/ 2 =

[100-10] /2 =

90/2 =

45

CPhill  Jan 31, 2015

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