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I got this solution while using Wolframalpha:

$$ (-1.66667 n+1/2-0.133333/n+0.0208/n^3-0.0127573/n^5+O((1/n)^6))/n^1.6+2.28577 $$

Could somebody tell me this solution step-by-step?

I need to write a function to calculate this.

Thank you!

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I have found the answer: describes that:

H_n^(1.6) = sum_(k=1)^n 1/k^r where r = 1.6

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