prove-that-n-1-H-n-n-2-2-3-with-x-n-1-1-n-x-and-x-gt-1-

Question Number 33892 by math khazana by abdo last updated on 26/Apr/18

p r o v e t h a t \sum_{n = 1}^{\infty} \frac{H_{n}}{n^{2}} = 2 ξ (3) w i t h

ξ (x) = \sum_{n = 1}^{\infty} \frac{1}{n^{x}} a n d x > 1 .

Commented by math khazana by abdo last updated on 26/Apr/18

H_{n} = \sum_{k = 1}^{n} \frac{1}{k} .