Let \( \{a_k\} \) and \( \{b_k\} , \ k \in e , \) be two G.P.s with common ratios \( r_1 \) and \( r_2 \) respectively such that \( a_1 - b_1 = 4 \) and \( r_1 < r_2 \). Let \( c_k = a_k + b_k , \ k \in \)\(\mathbb{N}\). If \( c_2 = 5 \) and \( c_3 = \frac{13}{4} \) then \( \displaystyle \sum_{k=1}^{\infty} c_k - (12a_6 + 8b_4) \) is equal to ________.
