Just asking...

[Ivars]

If in series there is 1/n!, then formula becomes:
n= ln(2) * ((1-exp(-x))/x)

if just 1/n, then:
n= ln(2) * (ln(1+x)/x)

Nope, neither of them worked. But hey, it was worth trying.

I may have been mistaken with formulas which I derived from series, the series of type ln(2)*(1- a*x +b*x^2 - c*x^3+..) itself looked more promising

May be it is just ln(2)-ln(2)/2*x.

Ivars