Given the recursion $u_{k+1}=\frac{1}{2}(3 u_k - u_{k-1})$ find the expression of $u_k$ in dependence on the values $u_0$ and $u_1$. What is the limit as $ k\rightarrow \infty$ of $\{u_k\}_{k}$? Give a possible biological interpretation of this recursion.
Hello,
I found the recursion $u_k= 2u_1-u_0 + 2(u_0-u_1)* (\frac{1}{2})^k$ and $\lim_{k\rightarrow \infty} u_k=2u_1-u_0$.
But what is missing is the biological interpration. We discuss last lecture time discrete models in population dynamics.$u_k$ means than the individuals in the kth generation. Did anyone know this recursion in this connection?