let-x-n-1-1-n-x-with-x-gt-1-1-prove-that-1-x-1-x-x-x-1-2-find-lim-x-1-x-1-x-

Question Number 34721 by abdo mathsup 649 cc last updated on 10/May/18

l e t ξ (x) = \sum_{n = 1}^{\infty} \frac{1}{n^{x}} w i t h x > 1

1) p r o v e t h a t \frac{1}{x - 1} ⩽ ξ (x) ⩽ \frac{x}{x - 1}

2) f i n d {l i m}_{x \to 1^{+}} (x - 1) ξ (x) .