Any efficient way to calculate the sum of harmonic series upto nth term? 1 + 1/2 + 1/3 + --- + 1/n =?

Question

Is there any formula for this series "1 + 1/2 + 1/3 + --- + 1/n = ?" I think it is a harmonic number in a form of sum(1/k) for k = 1 to n.

Answer 1

As it is the harmonic series summed up to n, you're looking for the nth harmonic number, approximately given by γ + ln[n], where γ is the Euler-Mascheroni constant.

For small n, just calculate the sum directly:

double H = 0;
for(double i = 1; i < (n+1); i++) H += 1/i;