Let $\left\{a_k\right\}$ and $\left\{b_k\right\}, k \in N$, be two G.P.s with common ratio $r_1$ and $r_2$ respectively such that $a_1=b_1=4$ and $r_1

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

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Let \(\left\{a_k\right\}\) and \(\left\{b_k\right\}, k \in N\), be two G.P.s with common ratio \(r_1\) and \(r_2\) respe…

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