f(X)=x^3+x+1 inverse f ?
Mmm - beats me how to do it manually though.
https://www.wolframalpha.com/input/?i=inverse+of+y%3Dx%5E3%2Bx%2B1
S=1/1+1/2+1/3+...+1/n
S(n) ?
+118690 
