The current price of a stock can be modeled by $P_0 = \frac{D_{1}}{r-g}$ where $D_1$ is the expected dividend, $r$ is the rate of return, and $g$ is the expected growth rate in the perpetuity. If $r
$\displaystyle P_0 = \sum_{t=1}^{N} \frac{D_{0}(1+g)^{t}}{(1+r)^{t}} + \frac{P_N}{(1+r)^{N}}$.
Is there anyway to simplify this?