Find the value of $\sqrt{4+\sqrt[3]{4+\sqrt[4]{4+\sqrt[5]{4+ ....... }}}}$ I have tried solving this question. It would be great if someone gives some idea about how to go about solving this question.

Two long comment, this question is related to other question, but it seems that there is no closed form from thier realively partiel answers:


Evaluating the sum $\lim_{n\to \infty}\sqrt[2]{2+\sqrt[3]{2+\sqrt[4]{2+\cdots+\sqrt[n]{2}}}}$


Problem 6 - IMO 1985


How to find this limit: $A=\lim_{n\to \infty}\sqrt{1+\sqrt{\frac{1}{2}+\sqrt{\frac{1}{3}+\cdots+\sqrt{\frac{1}{n}}}}}$


Find the limit $L=\lim_{n\to \infty} \sqrt{\frac{1}{2}+\sqrt[3]{\frac{1}{3}+\cdots+\sqrt[n]{\frac{1}{n}}}}$


