TeX source:

{\begin{aligned}\varepsilon _{i+1}&=1-DX_{i+1}\\&=1-D(X_{i}(2-DX_{i}))\\&=1-2DX_{i}+D^{2}X_{i}^{2}\\&=(1-DX_{i})^{2}\\&={\varepsilon _{i}}^{2}.\\\end{aligned}}