lean_workbook_plus_15360

Let sequence $(u_n)$ such that $u_1=\frac{1}{2}; u_{2}=3; u_{n+2} =\frac{u_{n+1}u_{n}+1}{u_{n+1}+u_{n}}$. a) Prove that $u_n>1, \forall n\in\mathbb{N}^*$. b) Find $\lim_{n\to \infty}u_{n}$