# Are there closed form solutions to the harmonic series?

1. Mar 22, 2005

### courtrigrad

Are there closed form solutions to the harmonic series?

2. Mar 22, 2005

### HallsofIvy

Staff Emeritus
Sure. The sum $$\Sigma_{k=1}^{n}\frac{1}{k}= \gamma+ \Psi_0(n+1)$$ where $$\gamma$$ is the "Euler-Mascheroni" constant and $$\Psi_0$$ is the digamma function. Or did you mean something else by "closed form"?

See
http://mathworld.wolfram.com/HarmonicSeries.html

3. Mar 22, 2005

### courtrigrad

yeah thats what i meant. thanks. also is most everything known about harmonic series? what is not known?

thanks

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