Two$-$Stage Dividend Growth $[[$ L$01]$ Regarding the two$-$stage dividend growth model in the chapter, show that the price of a share of stock today can be written as follows:

$P_0=\frac{D_0(1+g_1)}{R-g_1}[1-(\frac{1+g_1}{1+R}{)}^t]+(\frac{1+g_1}{1+R}{)}^t\frac{D_0(1+g_2)}{R-g_2}$