Chapter 9.8, Problem 63ES

If the constant p in the general p-series is replaced by a variable $xforx>1,$ then the resulting function is called the Riemann Zeta function and is denoted by $\varsigma (x)={\displaystyle \underset{k=1}{\overset{\infty }{\sum }}\frac{1}{k^x}}$

(a) Let $s_n$ be the $nth$ partial sum of the series for $\varsigma (3.7)$ to two decimal-place accuracy, and calculate $s_n$ using this value of $n.$

(b) Determine whether your CAS can evaluate the Riemann zeta function directly. If so, compare the value produced by the CAS to the value of $s_n$ obtained in part (a).