The zeta function is closely related to prime numbers. For example, the aforementioned fact that there are infinitely many primes can also be seen using the zeta function: if there were only finitely many primes then ζ(1) would have a finite value. However, the harmonic series 1 + 1/2 + 1/3 + 1/4 + ... diverges (i.e., exceeds any given number), so there must be infinitely many primes. Another example of the richness of the zeta function and a glimpse of modern algebraic number theory is the following identity (Basel problem), due to Euler,
What property of the harmonic series 1 + 1/2 + 1/3 + 1/4 + ... shows that there is an infinite number of primes?
diverges diverges exceeds any given number
diverges (i.e., exceeds any given number), so there must be infinitely many primes.
diverges (i.e., exceeds any given number), so there must be infinitely many primes.
What property of the harmonic series one + one/two + one/three + one/four + ... shows that there is an infinite number of primes?