In error I wrote: << Sum_{k = 1 to n} 1/k^s = (1/Gamma(s))*Integral_{0 to oo} ((1-u^n)/(1-u))) (ln(1/u))^(s-1) du.

...

but in fact the upper limit of the integral should be 1: Sum_{k = 1 to n} 1/k^s = (1/Gamma(s))*Integral_{0 to 1} ((1-u^n)/(1-u))) (ln(1/u))^(s-1) du.