Closed form expression to a nested radical formula

Asked Nov 16 '16 at 01:04

Active Nov 16 '16 at 01:04

Viewed 133 times

$$\large\lim\limits_{n\to\infty}\left(1+\sqrt{2+\sqrt[3]{3+\sqrt[4]{4+\sqrt[5]{5+\sqrt[6]{6+\cdots+\sqrt[n-1]{(n-1)+{\sqrt[n]{n}}}}}}}}\right)$$

I can only obtain the numerical approximation of it:

$$2.911639216245824$$

How to find a mostly simplified cloed form expression?

asked Nov 16 '16 at 01:04

user6043040

3

I would be surprised if this had a closed form expression. But I've been surprised before. – Robert Israel Nov 16 '16 at 01:13
2

Try to write it as a recursion. I dont know if this is possible. – Masacroso Nov 16 '16 at 01:15

0 Answers0