let-x-gt-1-and-x-n-1-1-n-x-zeta-function-of-Rieman-1-calculate-lim-x-x-2-let-consider-s-x-n-2-n-n-x-n-study-the-convergence-of-s-x-and-find-a-simple-form

Question Number 32487 by abdo imad last updated on 25/Mar/18

l e t x > 1 a n d ξ (x) = \sum_{n = 1}^{\infty} \frac{1}{n^{x}} (z e t a f u n c t i o n o f R i e m a n)

1) c a l c u l a t e {l i m}_{x \to + \infty} ξ (x)

2) l e t c o n s i d e r s (x) = \sum_{n = 2}^{\infty} \frac{ξ (n)}{n} x^{n} s t u d y t h e c o n v e r g e n c e

o f s (x) a n d f i n d a s i m p l e f o r m o f s (x) .