Compute the sum
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