Question on overlapping generations My question is from over lapping generations
Question is as follows

I found that
$$k(t+1)= \frac{\beta(1-\alpha)}{(1+\beta)(1+n)}A(t)k(t)^{\alpha}$$
How can I deal with A(t) to find the steady state $k^*$?
By the way, at steady state,$ k(t+1)=k(t)=k^*$
Is that derivation for $k(t+1)$ correct? Technically, you never reach the steady state, but only asimptotically as $t\rightarrow\infty$, but at infinity the $A(t)$ will also be infinite because it grows exponentially with time. I suspect that $k(t+1)$ should depend on $(1+g)$ instead of $A(t)$.
Usually these models are expressed in units of effective labor, that is, dividing the capital stock $K(t)$ and the labor $L(t)$ (and hence, the production and consumption) by $N(t)$ and $A(t)$.