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)