I would like to know how I can derive the third equation.

The slides show how to derive the price stock, but it fails to explain how to show it as a difference between the today's divident and the discounted future dividends.

he price of a stock with constant expected returns If expected returns are constant, then Et(Rt,t+k)=Rk and we get Pt=k=1RkEt(Dt+k) In the special case of a constant expected dividend, this further simplifies to: Pt=R1Dt More generally, for constant expected R we can write Pt=Dt1+rrEt(i=0(R1)iDt+i)