<s>[INST] We are given a sequence defined by $a_1 = 2$ and $a_n = \frac{a_{n-1}}{2} + \frac{1}{2} \cdot \left(\frac{1}{a_{n-1}}\right)$. If $S_n = \sum_{i=1}^{n} a_i$, find the value of $S_{10}$.[/INST]