1. Let $A=\left\{\frac{\sqrt{4}-\sqrt{2}}{\sqrt{8}}, \frac{\sqrt{6}-\sqrt{4}}{\sqrt{24}}, \frac{\sqrt{8}-\sqrt{6}}{\sqrt{48}}, \ldots, \frac{\sqrt{2014}-\sqrt{2012}}{\sqrt{2014 \cdot 2012}}\right\}$.

a) Calculate the sum of the elements of set A.

b) Show that for any subset B of set $A$, the sum of the elements of B cannot be a natural number.