money demand = Mt
Price Level = Pt
inflation sensitivity parameter = g (supposed to be gamma, but I don't know how to make one in Wiki)
log(Mt/Pt) = log(Pt+1/Pt)^g
log(Mt/Pt) = glog(Pt+1/Pt)
log Mt - log Pt = g (log Pt+1 - log Pt)
he takes out the log notation to make it look cleaner
Mt - Pt = g(Pt+1 - Pt)
express current price level as a function of money supply and future price level
Pt = (1/1+g)Mt + (g/1+g)Pt+1
if g = 0, the Pt = Mt (this is the quantity theory of money: the current money supply = the current price level and future money supply does not matter)
this last expression can be converted into an infinite series by updating, then substituting (i.e., update Pt to Pt+1 and sub back into the right side)