The Riemann zeta function, defined as ζ(s) = X∞ n = 11/ns is an extremely important function in mathematics (particularly number theory) and physics (string theory). While it has many applications, one of its primary uses is to estimate a distribution of prime numbers. It is the center of one of the greatest still-open problems in mathematics, called the Riemann Hypothesis (whose proof as true would be a giant boon to science).
(a) Determine if ζ(1) converges or diverges.