Equation Derivation: Help with intermediate steps
This is not directly related to signal processing, but similar calculations are ubiquitous in DSP. So, here we go:

$$\begin{align}e^{-n/D}\frac{1-e^{(n+1)/D}}{1-e^{1/D}}&amp;=\frac{e^{-n/D}-e^{1/D}}{1-e^{1/D}}\\&amp;=\frac{e^{1/D}}{e^{1/D}}\cdot\frac{e^{-(n+1)/D}-1}{e^{-1/D}-1}\\&amp;=\frac{1-e^{-(n+1)/D}}{1-e^{-1/D}}\end{align}$$