Arithmetic About Recursion

Discrete Mathematics Level 2

Let $k_1, k_2, \ldots,$ be a sequence that is recursively defined as $k_{n+2} = k_{n+1} + 2 k_{n}$ , for all $n\geq 1$ , with $k_1 = k_2 = 1$ . The infinite sum, $S = \frac{k_1}{7 ^1} + \frac{k_2}{7 ^2} + \frac{k_3}{7 ^3} \ldots$ , is a fraction of the form $\frac{a}{b}$ , where $a$ and $b$ are coprime integers. What is the value of $a+b$ ?