context: 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,
question: హార్మోనిక్ శ్రేణిలో 1 + 1/2 + 1/2 + 1/3 + 1/4 +... అంతులేని సంఖ్యలు ఉన్నాయని ఏ గుణకం చూపిస్తుంది?
answers: diverges diverges exceeds any given number