2.8.70 Power series

condition: Expand the function \( f(x) \) into a series in powers \( \left(x-x_{0}\right), \quad \) using ready-made expansions (i.e. without finding derivatives). In this case, it is necessary to obtain an expression for the general term of the series and indicate the region in which the resulting expansion is valid. \[ 3 x+\sqrt{-\frac{x}{2}}, \quad x_{0}=-1 \]