1. The problem is to understand the function defined by the Riemann zeta function $$\zeta(s) = \sum_{n=1}^\infty \frac{1}{n^s}$$ where $s$ is a complex number with real part greater than 1 for convergence. 2. This is an infinite series summing the terms $\frac{1}{n^s}$ starting from $n=1$ to infinity. 3. Important rule: The series converges when the real part of $s$ is greater than 1. 4. The function is fundamental in number theory and complex analysis, and it cannot be expressed in a simple closed form for general $s$. 5. For real $s > 1$, the series converges and can be approximated by partial sums. 6. For example, if $s=2$, then $$\zeta(2) = \sum_{n=1}^\infty \frac{1}{n^2} = \frac{\pi^2}{6} \approx 1.6449.$$