\[\boxed{\mathbf{1047}\mathbf{.}\mathbf{\ }}\]
\[\frac{2}{3 \cdot 5} + \frac{2}{5 \cdot 7} + .. + \frac{2}{29 \cdot 31} =\]
\[= \frac{1^{\backslash 31}}{3} - \frac{1^{\backslash 3}}{31} = \frac{31}{93} - \frac{3}{93} =\]
\[= \frac{31 - 3}{93} = \frac{28}{93}\]