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Is there a formula for calculating such a sequence of numbers: 1/1 + 1/2 + 1/3 + 1/4 + 1/5 + ... 1/x? I know that the sum of the Harmonic series is equal to infinity, but is there a formula for calculating a collection of numbers to a certain number, for example, to 1/49?

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    $\begingroup$ No simple closed formula is known. there are some good estimates, which you can read about, e.g., here $\endgroup$ – lulu Feb 11 at 17:18
  • $\begingroup$ wolframalpha.com/input/?i=49th+harmonic+number $\endgroup$ – Yves Daoust Feb 11 at 17:24
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    $\begingroup$ $\lim _{n\to \infty }\left(H_{n}-\ln n\right)=$ Euler-Mascheroni constant $\gamma \approx 0.5772156649$ $\endgroup$ – J. W. Tanner Feb 11 at 17:30

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