Let $\left\{ a _ { k } \right\}$ and $\left\{ b _ { k } \right\} , k \in \mathbb { N }$, be two G.P.s with common ratio $r _ { 1 }$ and $r _ { 2 }$ respectively such that $\mathrm { a } _ { 1 } = \mathrm { b } _ { 1 } = 4$ and $\mathrm { r } _ { 1 } < \mathrm { r } _ { 2 }$. Let $\mathrm { c } _ { \mathrm { k } } = \mathrm { a } _ { \mathrm { k } } + \mathrm { b } _ { \mathrm { k } } , \mathrm { k } \in \mathbb { N }$. If $\mathrm { c } _ { 2 } = 5$ and $\mathrm { c } _ { 3 } = \frac { 13 } { 4 }$ then $\sum _ { \mathrm { k } = 1 } ^ { \infty } \mathrm { c } _ { \mathrm { k } } - \left( 12 \mathrm { a } _ { 6 } + 8 \mathrm {~b} _ { 4 } \right)$ is equal to $\_\_\_\_$
Let $\left\{ a _ { k } \right\}$ and $\left\{ b _ { k } \right\} , k \in \mathbb { N }$, be two G.P.s with common ratio $r _ { 1 }$ and $r _ { 2 }$ respectively such that $\mathrm { a } _ { 1 } = \mathrm { b } _ { 1 } = 4$ and $\mathrm { r } _ { 1 } < \mathrm { r } _ { 2 }$. Let $\mathrm { c } _ { \mathrm { k } } = \mathrm { a } _ { \mathrm { k } } + \mathrm { b } _ { \mathrm { k } } , \mathrm { k } \in \mathbb { N }$. If $\mathrm { c } _ { 2 } = 5$ and $\mathrm { c } _ { 3 } = \frac { 13 } { 4 }$ then $\sum _ { \mathrm { k } = 1 } ^ { \infty } \mathrm { c } _ { \mathrm { k } } - \left( 12 \mathrm { a } _ { 6 } + 8 \mathrm {~b} _ { 4 } \right)$ is equal to $\_\_\_\_$