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

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Is there any formula for this series "1 +开发者_JAVA百科 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.

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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;

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If I understood you question correctly, reading this should help you: http://en.wikipedia.org/wiki/Harmonic_number

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Here's one way to look at it:

http://www.wolframalpha.com/input/?i=sum+1/j,+j%3D1+to+n

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function do(int n) 
{
    if(n==1)
        return n;

    return 1/n + do(--n); 
}