Question Number 49326 by Saorey last updated on 05/Dec/18
$$\mathrm{please}\:\mathrm{help}\:\mathrm{me}! \\ $$$$\begin{cases}{\mathrm{u}_{\mathrm{1}} ={a},\:\mathrm{u}_{\mathrm{2}} =\mathrm{b}}\\{\mathrm{u}_{\mathrm{n}+\mathrm{2}} =\mathrm{3}\sqrt[{\mathrm{5}}]{\mathrm{u}_{\mathrm{n}+\mathrm{1}} }+\mathrm{13}\sqrt[{\mathrm{5}}]{\mathrm{u}_{\mathrm{n}} }\:,\mathrm{n}\in\mathbb{N}^{\ast} }\end{cases} \\ $$$$\mathrm{show}\:\mathrm{that}\:\left(\mathrm{u}_{\mathrm{n}} \right)\:\mathrm{have}\:\mathrm{limit}\:\mathrm{and}\:\mathrm{find}\: \\ $$$$\mathrm{its}\:\mathrm{limit}. \\ $$