Is there a partial sum formula for the Harmonic Series? [duplicate]

sequences-and-series summation harmonic-numbers

No, there is no nice closed form for the harmonic numbers. There are some very accurate approximations that are easily computed;

$$H_n\approx\ln n+\gamma+\frac1{2n}-\frac1{12n^2}$$

is quite good, where $\gamma\approx 0.5772156649$ is the Euler-Mascheroni constant.

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