Can you notice a pattern?

Clearly the question involves concept of G.P. And so the solution will contain formula for summation of a G.P.I am not mentioning the formula here and directly using it in my solution.

Note that the series contains infinite terms!

Rearranging the terms we get

${ s }_{ 1 }=\cfrac { 1 }{ 7 } +\cfrac { 1 }{ { 7 }^{ 3 } } +...=\cfrac { { 1 }/{ 7 } }{ 1-\left( { 1 }/{ { 7 }^{ 2 } } \right) } =\cfrac { 7 }{ 48 } \\ { s }_{ 2 }=\cfrac { 2 }{ { 7 }^{ 2 } } +\cfrac { 21 }{ { 7 }^{ 4 } } +...=\cfrac { { 2 }/{ { 7 }^{ 2 } } }{ 1-\left( { 1 }/{ { 7 }^{ 2 } } \right) } =\cfrac { 2 }{ 48 } \\ s={ s }_{ 1 }+{ s }_{ 2 }=\cfrac { 7 }{ 48 } +\cfrac { 2 }{ 48 } =\cfrac { 3 }{ 16 }$