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Partial sums of harmonic series

Posted 9 years ago

https://www.wolframalpha.com/input/?i=sum+1%2Fj%2C+j%3D1+to+132159290357566703

How wolfram alpha calculates something like this? Brute force, or has some kind of formula?

POSTED BY: Ivan Miški?

An integral representation derived by Euler gives H_n = Integrate[(1-x^n)/(1-x),{x,0,1)]

The limit n -> infinity (H_n - log n) = gamma, the Euler-Mascheroni constant 0.5772...

POSTED BY: S M Blinder
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