Simplify the following expression and find the value of a + b:

If \[ \sqrt{1+\frac{1}{4}+\frac{2}{2}} + \sqrt{1+\frac{1}{36}+\frac{2}{6}} + \sqrt{1+\frac{1}{144}+\frac{2}{12}} + \cdots + \sqrt{1+\frac{1}{8100}+\frac{2}{90}} = \frac{a}{b} \] where \(a\) and \(b\) are co-primes, then what is the value of \(a + b\)?