Complexity of $x+\log x+\log(\log x)+...+\log(\log(\log(...(\log x)...)))$

71 Views Asked by At

Formally, we define a sequence of functions $(f_n)$ such that $f_0(x) = x$ and $f_{a+1}(x) = \log(f_a(x))$.

What is $$\text{O}\left(\sum_{i=0}^n f_i(n)\right)?$$