$ c_2 = s\left(\frac{1}{2}\right) = \frac{1}{2} - \frac{1}{5} \left(\frac{1}{2}\right)^5 = \frac{1}{2} - \frac{1}{5} \cdot \frac{1}{32} = \frac{1}{2} - \frac{1}{160} = \frac{80 - 1}{160} = \frac{79}{160} $