$$\lim_{n\to\infty}1+\sqrt[2]{2+\sqrt[3]{3+\sqrt[4]{4+\ldots+\sqrt[n]{n}}}}$$
I have no idea about this.
The equation can be written in its recursive form as:
$$f(n) = g(1,n)$$
Where
$$g(x,n) = [x\impliedby n]\cdot (x+ g(x+1,n))^{\frac 1x}+[x=n]\cdot (n)^{\frac 1n}$$
Of course, [] is the indicator function representing of piece wise notation.