@tomleslie 

Actually, what I'm tring to solve goes the other way around. Given

p[t] = psi*E(p[t+1])/(1+psi)+m[t]/(1+psi)

where 

E(p[t+1]) = psi*E(p[t+2])/(1+psi)+m[t+2]/(1+psi)

If I limit the recursion to 1 I would get

p[t] = psi*(psi*E(p[t+2])/(1+psi)+m[t+2]/(1+psi))/(1+psi)+m[t]/(1+psi)

If it let it go to two levels I would get

p[t] = psi*(psi*(psi*p[t+3]/(1+psi)+m[t+3]/(1+psi))/(1+psi)+m[t+2]/(1+psi))/(1+psi)+m[t]/(1+psi)

and so on.

I'd like maple to help me expand to n levels, simplifying the expression and finally evaluating for a specific m (either a constant value or a function of t). I would then prove that for a constant m, the expansion converges.