=\frac{e^{-\lambda}}{\lambda}\cdot\left(\sum\limits_{n=0}^{\infty}{\frac{\lambda^n}{n!}}-\frac{\lambda^0}{0!}\right)=\frac{e^{-\lambda}}{\lambda}\cdot\left(e^{\lambda}-1\right)=\frac{1-e^{-\lambda}}{\lambda}