\begin{aligned}\frac{E_{i}}{c} & = −\frac{E_{f}}{c} + γm_{e}v \\ E_{i} + m_{e}c^{2} & = E_{f} + γm_{e}c^{2} \end{aligned}

\frac{1}{E_{f}} = \frac{1}{E_{i}} + \frac{2}{m_{e}c^{2}}

\frac{1}{E_{f}} ≃ \frac{1}{∞} + \frac{2}{m_{e}c^{2}}

E_{f} ≃ \frac{m_{e}c^{2}}{2}

\frac{E_{i}}{E_{f}} ≃ \frac{1}{2} (1 − \frac{v}{c} )