Find the limit \[\lim_{n\to \infty}\sqrt{5+1\smash[b]{\sqrt{6+2\smash[b]{\sqrt{7+3\smash[b]{\sqrt{\ldots \smash[b]{\sqrt{(n+3)+(n-1)\smash[b]{\sqrt{n+4+n^n}}}}}}}}}}}.\] We have not received any solutions. The limit in question is equal to $3$. For a complete solution see the following link {{:pow:2022sproblem7.pdf|Solution}}.