If $a_1, a_2, \dots, a_n$ is an arithmetic progression with common difference $d$, find the sum: $S = \frac{1}{\sqrt{a_1} + \sqrt{a_2}} + \frac{1}{\sqrt{a_2} + \sqrt{a_3}} + \dots + \frac{1}{\sqrt{a_{n-1}} + \sqrt{a_n}}$.