$F(z)=\frac{1}{1-z}$, when expanded as a power series around $z=2$, would result in $F(z)=\sum_{k=0}^{\infty} a_k(z-2)^k$, with the region of convergence $\text{(ROC) } |z-2|<1$. The coefficients $a_k, k \geq 0$, are given by the expression _____________.
- $(-1)^k$
- $(-1)^{k+1}$
- $\left(\frac{1}{2}\right)^k$
- $\left(\frac{-1}{2}\right)^{k+1}$